"Evaluate the following integrals. ∫0116x42xdx" was answered by our community

sjeikdom0

Answered question

2021-03-09

Evaluate the following integrals.

\int_{0}^{1} \frac{16^{x}}{4^{2 x}} d x

toroztatG

Skilled2021-03-10Added 98 answers

To integrate: \int_{0}^{1} \frac{16^{x}}{4^{2 x}} d x

Solution:

\int_{0}^{1} \frac{16^{x}}{4^{2 x}} d x

Om simplifying further we get:

\int_{0}^{1} \frac{16^{x}}{4^{2 x}} d x = \int_{0}^{1} \frac{(4^{2})^{x}}{4^{2 x}} d x

= \int_{0}^{1} \frac{4^{2 x}}{4^{2 x}} d x

= \int_{0}^{1} 1 d x

= [x]_{0}^{1}

= [1 - 0]

= 1

Result: \int_{0}^{1} \frac{16^{x}}{4^{2 x}} d x = 1

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