Exercise 11.1-Additional Questions - Chapter 11 Integral Calculus 11th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated By SaraNextGen

On April 24, 2024, 11:35 AM

Additional Problems
Integrate the following with respect to $\mathrm{x}$.
Question 1.
(i) $\sqrt{x^7}$
(ii) $\left(x^{10}\right)^{1 / 7}$
Solution:
(i) $\int \sqrt{x^7} d x=\int\left(x^7\right)^{1 / 2} d x=\int x^{7 / 2} d x=\frac{x^{7 / 2+1}}{7 / 2+1}=\frac{x^{9 / 2}}{9 / 2}=\frac{2}{9} x^{9 / 2}+c$
(ii) $\int\left(x^{10}\right)^{1 / 7} d x=\int x^{10 / 7} d x=\frac{x^{10 / 7+1}}{10 / 7+1}=\frac{x^{17 / 7}}{17 / 7}=\frac{7}{17} x^{17 / 7}+c$
Question 2.
(i) $\frac{1}{x^5}$
(ii) $\mathrm{x}^{-1}$
(iii) $\frac{1}{x^{5 / 2}}$

Solution:
(i) $\int \frac{1}{x^5} d x=\int x^{-5} d x=\frac{x^{-5+1}}{-5+1}=\frac{x^{-4}}{-4}=\frac{-1}{4 x^4}+c$
(ii) $\int x^{-1} d x=\int \frac{1}{x} d x=\log x+c$
(iii) $\int x^{-5 / 2} d x=\frac{x^{-5 / 2+1}}{-5 / 2+1}=\frac{x^{-3 / 2}}{-3 / 2}=\frac{-2}{3 x^{3 / 2}}+c$