Get the answer to "Evaluate the definite integral. ∫08e2xdx"

signokodo7h

Answered question

2021-11-16

Evaluate the definite integral.

\int_{0}^{8} e^{2 x} d x

Opeance1951

Beginner2021-11-17Added 26 answers

Step 1
The integral of

e^{x} i s e^{x}

so the integral of

e^{a x}

is (1/a)

e^{a x}

.
Using this we can integrate the given function.
Step 2

\int_{0}^{8} e^{2 x} d x [\int e^{a x} d x = \frac{e^{a x}}{a} + c]

= {[\frac{e^{2 x}}{2}]}_{0}^{8}

= \frac{1}{2} {[e^{2 x}]}_{0}^{8}

= \frac{1}{2} [e^{2 \times 8} - e^{2 \times 0}]

= \frac{1}{2} [e^{16} - 1]

= \frac{e^{16} - 1}{2}

\int_{0}^{8} e^{2 x} d x = \frac{e^{16} - 1}{2}

Kevin Hunt

Beginner2021-11-18Added 20 answers

Step 1: If f(x) is a continuous function from a to b, and if F(x) is its integral, then:

\int_{a}^{b} f (x) d x = F (x) ∣_{a}^{b} = F (b) - F (a)

Step 2: In this case,

f (x) = e^{2 x}

. Find its integral.

\frac{e^{2 x}}{2} ∣_{0}^{8}

Step 3: Since

F (x) ∣_{a}^{b} = F (b) - F (a)

, expand the above into F(8)−F(0):

\frac{e^{2 \times 8}}{2} - \frac{e^{2 \times 0}}{2}

Step 4: Simplify.

\frac{e^{16}}{2} - \frac{1}{2}

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