Solveeit Logo
Login

Question

Question: Which of the following is not correct?...

Which of the following is not correct?

A

∫−aax.(f(cos⁡x))2.dx\int_{- a}^{a}{x.(f(\cos x))^{2}.dx} = 0

B

∫0nπf(cos⁡2x)dx\int_{0}^{n\pi}{f(\cos^{2}x)dx} = n∫0πf(cos⁡2x)dxn\int_{0}^{\pi}{f(\cos^{2}x)dx} n ĪN

C

∫0b−cf(x+c)dx\int_{0}^{b - c}{f(x + c)dx} = ∫bcf(x)dx\int_{b}^{c}{f(x)dx}

D

∫aπ−ax.f(sin⁡x)dx\int_{a}^{\pi - a}{x.f(\sin x)dx} = π2∫aπ−af(sin⁡x)dx\frac{\pi}{2}\int_{a}^{\pi - a}{f(\sin x)dx}

Answer

∫0b−cf(x+c)dx\int_{0}^{b - c}{f(x + c)dx} = ∫bcf(x)dx\int_{b}^{c}{f(x)dx}

Explanation

Solution

Note that ∫0b−cf(x+c)dx\int_{0}^{b - c}{f(x + c)dx} = −∫bcf(x)dx- \int_{b}^{c}{f(x)dx}