Answered: "Evaluate the definite integral. ∫232xdx"

High School
Calculus and Analysis
Calculus 2
Applications of integrals

Terrie Lang

Answered question

2021-12-28

Evaluate the definite integral.

\int_{2}^{3} 2^{x} d x

Answer & Explanation

Stella Calderon

Beginner2021-12-29Added 35 answers

Step 1
To evaluate the given integral,

\int_{2}^{3} 2^{x} d x

Solution:
The given integral is,

\int_{2}^{3} 2^{x} d x

Solving integral we get,

\int_{2}^{3} 2^{x} d x = {\frac{2^{x}}{\log 2}}_{2}^{3}

= \frac{2^{3} - 2^{2}}{\log 2}

= \frac{8 - 4}{\log 2}

Step 2
further solving we get,

\int_{2}^{3} 2^{x} d x = 4 \log 2

Hence, the value of integral is

\frac{4}{\log 2}

Kirsten Davis

Beginner2021-12-30Added 27 answers

Given:

\int_{2}^{3} 2^{x} d x

Integral of exponential function:

\int a^{x} d x = \frac{a^{x}}{\ln (a)}

at a=2:

= \frac{2^{x}}{\ln (2)}

Answer:

= \frac{2^{x}}{\ln (2)} + C

Vasquez

Expert2022-01-07Added 669 answers

$\int_{2}^{3} 2^{x} d x$
$\int 2^{x} d x$
$\frac{2^{x}}{\ln (2)}$
Return the limits
$\frac{2^{x}}{\ln (2)} |_{2}^{3}$
Calculate the expression
$\frac{2^{3}}{\ln (2)} - \frac{2^{2}}{\ln (2)}$
Simplify
Solution
$\frac{4}{\ln (2)}$

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