IXL - Evaluate definite integrals involving trigonometric functions (Calculus practice)

Evaluate the integral. Write an exact, simplified answer.

∫

–

sec

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Learn with an example

question

Evaluate the integral. Write an exact, simplified answer.

∫

–

csc

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 trigonometric functions.

∫
cos
x

d
x
=
sin
x
+
C
∫
sin
x

d
x
=
–
cos
x
+
C
∫
sec
2
x

d
x
=
tan
x
+
C
∫
csc
2
x

d
x
=
–
cot
x
+
C
∫
sec
x
tan
x

d
x
=
sec
x
+
C
∫
csc
x
cot
x

d
x
=
–
csc
x
+
C

solution

You were asked to evaluate

∫

–

csc

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

∫

–

csc

(

cot

)

cot

–

cot

–

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Not feeling ready yet? These can help:

R.2Fundamental Theorem of Calculus, Part 2

S.4Find indefinite integrals involving trigonometric functions

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