Evaluate the following integrals. int_0^1frac{16^x}{4^{2x}}dx

Evaluate the following integrals. int_0^1frac{16^x}{4^{2x}}dx

Question
Integrals
asked 2021-03-09
Evaluate the following integrals.
\(\int_0^1\frac{16^x}{4^{2x}}dx\)

Answers (1)

2021-03-10
\(\text{To integrate: }\int_0^1\frac{16^x}{4^{2x}}dx\)
\(\text{Solution:}\)
\(\int_0^1\frac{16^x}{4^{2x}}dx\)
\(\text{Om simplifying further we get:}\)
\(\int_0^1\frac{16^x}{4^{2x}}dx=\int_0^1\frac{(4^2)^x}{4^{2x}}dx\)
\(=\int_0^1\frac{4^{2x}}{4^{2x}}dx\)
\(=\int_0^1 1dx\)
\(=[x]_0^1\)
\(=[1-0]\)
\(=1\)
\(\textbf{Result: }\int_0^1\frac{16^x}{4^{2x}}dx=1\)
0

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