Use symmetry to evaluate the following integrals. \int_{\frac{-\pi}{4}}^{\frac{\pi}{4}}\tan 0 d0

Chesley

Chesley

Answered question

2021-10-18

Use symmetry to evaluate the following integrals.
π4π4tan0d0

Answer & Explanation

Yusuf Keller

Yusuf Keller

Skilled2021-10-19Added 90 answers

Step 1
NSK
The integral is π4π4tan0d0.
Check if the function is odd or even.
Substitute −θ for θ in the function f(θ)=tanθ.
f(0)=tan(0)
=tan0
Since, f(0)=f(0), so the function is an odd function.
Step 2
As per symmetry, if f is an odd function, then aaf(x)dx=0.
Thus,
π4π4tan0d0=0
Thus, the integral value is 0.

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