Use the wise properties

Calculus Level 3

$\large \displaystyle \int_{-2\pi}^{5\pi} \cot^{-1}(\tan x) \, dx=\, ?$

\frac{3 \pi}{2}

\frac{7\pi^2}{2}

\pi^2

\frac{7\pi}{2}

1 solution

Akhil Bansal
Nov 30, 2015

$\large I = \displaystyle \int_{-2\pi}^{5\pi} \cot^{-1}(\tan x) \, dx \quad \ \ \ \ldots \boxed{1}$ $\large I = \displaystyle \int_{-2\pi}^{5\pi} \cot^{-1}(\tan (3\pi - x ) \, dx$ $\large I = \displaystyle \int_{-2\pi}^{5\pi} \cot^{-1}(-\tan x) \, dx$ $\large I = \displaystyle \int_{-2\pi}^{5\pi}(\pi - \cot^{-1}(\tan x)) \, dx \quad \ \ \ \ldots \boxed {2}$ Add $\boxed{1}$ and $\boxed{2}$ , $\large 2I = \displaystyle \int_{-2\pi}^{5\pi} \pi \, dx$ $\large I = \dfrac{7\pi^2}{2}$

@Sandeep Bhardwaj This would depend on which cotangent function you use. My answer for this problem is 0.

Calvin Lin Staff - 5 years, 6 months ago

Use the wise properties

1 solution

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