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On March 11, 2024, 11:35 AM

Exercise 7.3 - Chapter 7 Integrals class 12 ncert solutions Maths - SaraNextGen [2024]


Question 1:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7510/NCERT_Solution_Math_Chapter_7_final_html_158e4d81.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7510/NCERT_Solution_Math_Chapter_7_final_html_m25ad4f6f.gif

Question 2:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7520/NCERT_Solution_Math_Chapter_7_final_html_m79d80b67.gif

Answer:

It is known that, https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7520/NCERT_Solution_Math_Chapter_7_final_html_e048a77.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7520/NCERT_Solution_Math_Chapter_7_final_html_4e6849bf.gif

Question 3:

cos 2x cos 4x cos 6x

Answer:

It is known that,https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7523/NCERT_Solution_Math_Chapter_7_final_html_mf795f95.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7523/NCERT_Solution_Math_Chapter_7_final_html_m453c4158.gif

Question 4:

sin3 (2x + 1)

Answer:

Let https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7525/NCERT_Solution_Math_Chapter_7_final_html_m634ea88b.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7525/NCERT_Solution_Math_Chapter_7_final_html_2257b9f2.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7525/NCERT_Solution_Math_Chapter_7_final_html_m5795a85f.gif

Question 5:

sin3 x cos3 x

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7527/NCERT_Solution_Math_Chapter_7_final_html_m73e75233.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7527/NCERT_Solution_Math_Chapter_7_final_html_69753c1b.gif

Question 6:

sin x sin 2x sin 3x

Answer:

It is known that, https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7529/NCERT_Solution_Math_Chapter_7_final_html_4735bd7c.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7529/NCERT_Solution_Math_Chapter_7_final_html_4b01ff05.gif

Question 7:

sin 4x sin 8x

Answer:

It is known that,

sin A . sin B = 12cosA-B-cosA+B∴∫sin4x sin8x dx=∫12cos4x-8x-cos4x+8xdx=12∫cos-4x-cos12xdx=12∫cos4x-cos12xdx=12sin4x4-sin12x12+C

Question 8:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7533/NCERT_Solution_Math_Chapter_7_final_html_4d6e72c3.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/content_ck_images/images/Kayako_FKY%2019079408.gif

Question 9:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7535/NCERT_Solution_Math_Chapter_7_final_html_7705fbfd.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7535/NCERT_Solution_Math_Chapter_7_final_html_m316e357f.gif

Question 10:

sin4 x

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7536/NCERT_Solution_Math_Chapter_7_final_html_m48648a1c.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7536/NCERT_Solution_Math_Chapter_7_final_html_m31f5f804.gif

Question 11:

cos4 2x

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7538/NCERT_Solution_Math_Chapter_7_final_html_m2f3cf2d6.gif

Question 12:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7540/NCERT_Solution_Math_Chapter_7_final_html_639207d4.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7540/NCERT_Solution_Math_Chapter_7_final_html_1b7154f9.gif

Question 13:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7543/NCERT_Solution_Math_Chapter_7_final_html_m3bf74025.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7543/NCERT_Solution_Math_Chapter_7_final_html_m3df62037.gif

Question 14:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7544/NCERT_Solution_Math_Chapter_7_final_html_m2f3df7c7.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7544/NCERT_Solution_Math_Chapter_7_final_html_m3ed05535.gif

Question 15:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7547/NCERT_Solution_Math_Chapter_7_final_html_61e38253.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7547/NCERT_Solution_Math_Chapter_7_final_html_m3ab061dc.gif

Question 16:

tan4x

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7549/NCERT_Solution_Math_Chapter_7_final_html_m781709fe.gif

From equation (1), we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7549/NCERT_Solution_Math_Chapter_7_final_html_m15daa35b.gif

Question 17:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7552/NCERT_Solution_Math_Chapter_7_final_html_390003e3.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7552/NCERT_Solution_Math_Chapter_7_final_html_m4da9ac1c.gif

Question 18:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7554/NCERT_Solution_Math_Chapter_7_final_html_m4c746474.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7554/NCERT_Solution_Math_Chapter_7_final_html_2529779e.gif

Question 19:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7557/NCERT_Solution_Math_Chapter_7_final_html_m473f7a6d.gif

Answer:

1sinxcos3x=sin2x+cos2xsinxcos3x=sinxcos3x+1sinxcosx

 

⇒1sinxcos3x=tanxsec2x+1cos2xsinxcosxcos2x=

tanxsec2x+sec2xtanx

https://img-nm.mnimgs.com/img/study_content/content_ck_images/images/zafar1111.png

Question 20:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7559/NCERT_Solution_Math_Chapter_7_final_html_3ac37af4.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7559/NCERT_Solution_Math_Chapter_7_final_html_m57da292d.gif

Question 21:

sin−1 (cos x)

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7562/item_82_html_5ca185ec.gif

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7562/item_82_html_34c59b7.gif

It is known that,

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7562/item_82_html_67f31dd1.gif

Substituting in equation (1), we obtain

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7562/item_82_html_62bbad50.gif

Question 22:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7564/NCERT_Solution_Math_Chapter_7_final_html_m299efddf.gif

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7564/NCERT_Solution_Math_Chapter_7_final_html_m6d95357.gif

Question 23:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7566/NCERT_Solution_Math_Chapter_7_final_html_m356fefc4.gif  is equal to

A. tan x + cot x + C

B. tan x + cosec x + C

C. − tan x + cot x + C

D. tan x + sec x + C

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7566/NCERT_Solution_Math_Chapter_7_final_html_m5794483e.gif

Hence, the correct Answer is A.

Question 24:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7568/NCERT_Solution_Math_Chapter_7_final_html_m28f9787.gif  equals

A. âˆ’ cot (exx) + C

B. tan (xex) + C

C. tan (ex) + C

D. cot (ex) + C

Answer:

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7568/NCERT_Solution_Math_Chapter_7_final_html_m46251d8.gif

Let exx = t

https://img-nm.mnimgs.com/img/study_content/curr/1/12/15/236/7568/NCERT_Solution_Math_Chapter_7_final_html_m410bc16d.gif

Hence, the correct Answer is B.

Also Read : Exercise-7.4-Chapter-7-Integrals-class-12-ncert-solutions-Maths

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