Use the given substitution to evaluate the integral. \int \sec^{2}(20)\tan(20)d0, u=\tan(20)

nitraiddQ

nitraiddQ

Answered question

2021-10-12

Use the given substitution to evaluate the integral.
sec2(20)tan(20)d0,u=tan(20)

Answer & Explanation

Nola Robson

Nola Robson

Skilled2021-10-13Added 94 answers

Step 1
Given integral:
sec2(20)tan(20)d0
Step 2
Substitute the u=tan(2θ) and differentiate it w.r.t θ
dud0=dd0tan(20)
dud0=2sec2(20)
sec2(20)d0=du2
So, we get
12udu...(1)
Step 3
Integrate the equation (1)
u24+C
Where, "C" is integrating constant.
tan2(20)4+C

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