Evaluate the following integrals. int_0^{pi/2}4^{sin x}cos xdx

Evaluate the following integrals. int_0^{pi/2}4^{sin x}cos xdx

Question
Integrals
asked 2021-02-06
Evaluate the following integrals.
\(\int_0^{\pi/2}4^{\sin x}\cos xdx\)

Answers (1)

2021-02-07
\(\text{Integration}\)
\(\int_0^{\pi/2}4^{\sin x}\cos xdx\)
\(\text{Let us take a substitution}\)
\(\sin x=z\)
\(\cos x dx=dz\)
\(\int_0^1 4^zdz\)
\(=[\frac{4^z}{\ln 4}]_0^1=\frac{4}{\ln4}-\frac{1}{\ln4}\)
\(=\frac{3}{\ln4}\)
\(\text{This is the required answer.}\)
0

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