IXL - Evaluate definite integrals involving exponential and logarithmic functions (Calculus practice)

Evaluate the integral. Write an exact, simplified answer.

∫

–

ref_doc_title.

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question

Evaluate the integral. Write an exact, simplified answer.

∫

–

key idea

The Fundamental Theorem of Calculus, Part

states that if

is a continuous function on

[

]

then

∫

(

)

(

)

–

(

)

where

(

)

is an antiderivative of

(

)

Remember that

(

)

is an antiderivative of

(

)

′

(

)

(

)

Here are some formulas for integrals that involve exponential and logarithmic functions.

∫
e
x

d
x
=
e
x
+
C
∫
a
x

d
x
=
a
x
ln
a
+
C
; a > 0 and a ≠ 1
∫
d
x
x
=
ln
absolute value bar
x
absolute value bar
+
C

solution

You were asked to evaluate

∫

–

First, find an antiderivative of the integrand. Then, evaluate the definite integral using the Fundamental Theorem of Calculus.

∫

–

(

)

–

(

)

–

(

–

)

(

)

–

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Not feeling ready yet? These can help:

S.3Find indefinite integrals involving exponential and logarithmic functions

R.2Fundamental Theorem of Calculus, Part 2

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