\(\text{To integrate: }\int_0^1\frac{16^x}{4^{2x}}dx\)

\(\text{Solution:}\)

\(\int_0^1\frac{16^x}{4^{2x}}dx\)

\(\text{Om simplifying further we get:}\)

\(\int_0^1\frac{16^x}{4^{2x}}dx=\int_0^1\frac{(4^2)^x}{4^{2x}}dx\)

\(=\int_0^1\frac{4^{2x}}{4^{2x}}dx\)

\(=\int_0^1 1dx\)

\(=[x]_0^1\)

\(=[1-0]\)

\(=1\)

\(\textbf{Result: }\int_0^1\frac{16^x}{4^{2x}}dx=1\)

\(\text{Solution:}\)

\(\int_0^1\frac{16^x}{4^{2x}}dx\)

\(\text{Om simplifying further we get:}\)

\(\int_0^1\frac{16^x}{4^{2x}}dx=\int_0^1\frac{(4^2)^x}{4^{2x}}dx\)

\(=\int_0^1\frac{4^{2x}}{4^{2x}}dx\)

\(=\int_0^1 1dx\)

\(=[x]_0^1\)

\(=[1-0]\)

\(=1\)

\(\textbf{Result: }\int_0^1\frac{16^x}{4^{2x}}dx=1\)