int_{-3}^{3} cot^{-1} x , dx = | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $ I = \int_{-3}^{3} \cot^{-1} x \, dx $. Using the property $ \int_{-a}^{a} f(x) \, dx = \int_{-a}^{a} f(-x) \, dx $ is not directly applicabl

Vedclass · Accepted Answer

$ 3\pi $

Vedclass · Answer

(C) Let $ I = \int_{-3}^{3} \cot^{-1} x \, dx $. Using the property $ \int_{-a}^{a} f(x) \, dx = \int_{-a}^{a} f(-x) \, dx $ is not directly applicable here,but we know that $ \cot^{-1}(-x) = \pi - \cot^{-1} x $. Consider the integral $ I = \int_{-3}^{3} \cot^{-1} x \, dx $. Using the property $ \int_{a}^{b} f(x) \, dx = \int_{a}^{b} f(a+b-x) \, dx $,we get: $ I = \int_{-3}^{3} \cot^{-1}(-x) \, dx = \int_{-3}^{3} (\pi - \cot^{-1} x) \, dx $. $ I = \int_{-3}^{3} \pi \, dx - \int_{-3}^{3} \cot^{-1} x \, dx $. $ I = \pi [x]_{-3}^{3} - I $. $ 2I = \pi (3 - (-3)) $. $ 2I = 6\pi $. $ I = 3\pi $.

$ \int_{-3}^{3} \cot^{-1} x \, dx = $

Similar Questions

$\int_{0}^{\pi} e^{\sin^2 x} \cos^3 x \, dx$ is equal to

The value of $\int_{0}^{4042} \frac{\sqrt{x} \, dx}{\sqrt{x}+\sqrt{4042-x}}$ is equal to

$\int_{\log \frac{1}{2}}^{\log 2} \sin \left(\frac{e^x-1}{e^x+1}\right) d x=$

If $I_n = \int_{0}^{\pi} \frac{\sin(nx)}{\sin(x)} dx$,then the value of $\sum_{n=1}^{10} I_n$ is-

If $\int_0^{10} f(x) d x=5$,then $\sum_{k=1}^{10} \int_0^1 f(k-1+x) d x=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module