how would you evaluate $int\tan^{20}xsec^{2}x dx$?\n\nchoose the correct answer.\n\na. use u = tan x.\nb…
how would you evaluate $int\tan^{20}xsec^{2}x dx$?\n\nchoose the correct answer.\n\na. use u = tan x.\nb. rewrite the power of tan x in terms of sec x. then use u = sec²x.\nc. use u = sec x.\nd. rewrite the power of sec x in terms of tan x. then use u = tan²⁰x.
Answer
Explanation:
Step1: Recall derivative of tangent
The derivative of $\tan x$ is $\sec^{2}x$, i.e., $d(\tan x)=\sec^{2}x dx$.
Step2: Apply substitution
In the integral $\int\tan^{20}x\sec^{2}x dx$, if we let $u = \tan x$, then $du=\sec^{2}x dx$. The integral becomes $\int u^{20}du$.
Answer:
A. Use $u = \tan x$