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Evaluate the integral ∫_ ^ sin^4x cos^3x dx. …
Related Topics
Wize University Calculus 1 Textbook > Integration Techniques
Trigonometric Integrals
10 Activities
Evaluate the integral
∫
sin
4
x
cos
3
x
d
x
\displaystyle\int_{ }^{ }\sin^4x\ \cos^3x\ dx
∫
sin
4
x
cos
3
x
d
x
.
sin
5
x
5
+
sin
7
x
7
+
C
\frac{\sin^5x}{5}+\frac{\sin^7x}{7}+C
5
s
i
n
5
x
+
7
s
i
n
7
x
+
C
sin
5
x
5
−
sin
4
x
4
+
C
\frac{\sin^5x}{5}-\frac{\sin^4x}{4}+C
5
s
i
n
5
x
−
4
s
i
n
4
x
+
C
sin
5
x
5
+
sin
4
x
4
+
C
\frac{\sin^5x}{5}+\frac{\sin^4x}{4}+C
5
s
i
n
5
x
+
4
s
i
n
4
x
+
C
sin
5
x
5
−
sin
7
x
7
+
C
\frac{\sin^5x}{5}-\frac{\sin^7x}{7}+C
5
s
i
n
5
x
−
7
s
i
n
7
x
+
C
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More Trigonometric Integrals Questions:
Practice Question: Trig Integral
Compute
∫
sec
6
x
d
x
{\displaystyle\int}\sec^6x\de{x}
∫
sec
6
x
d
x
.
Practice Question: Trig Integral
Compute
∫
sec
6
x
d
x
{\displaystyle\int}\sec^6x\de{x}
∫
sec
6
x
d
x
.
Practice Question: Trig Integral
Practice Question
Compute
∫
sin
7
x
d
x
{\displaystyle\int}\sin^7x\de{x}
∫
sin
7
x
d
x
.
Fraction with Cot and Sin
Evaluate
∫
cot
4
x
sin
4
x
d
x
\displaystyle\int\frac{\cot^4x}{\sin^4x}dx
∫
sin
4
x
cot
4
x
d
x
Evaluate the integral
∫
sin
4
x
cos
3
x
d
x
\displaystyle\int_{ }^{ }\sin^4x\ \cos^3x\ dx
∫
sin
4
x
cos
3
x
d
x
.
Evaluate the integral
∫
tan
2
x
sec
4
x
d
x
\displaystyle\int_{ }^{ }\tan^2x\sec^4x\ dx
∫
tan
2
x
sec
4
x
d
x
.
Practice Question: Trig Integral
Practice Question
Compute
∫
sin
7
x
d
x
{\displaystyle\int}\sin^7x\de{x}
∫
sin
7
x
d
x
.
Practice Question: Trig Integral
Practice Question
Compute
∫
sec
6
x
d
x
{\displaystyle\int}\sec^6x\de{x}
∫
sec
6
x
d
x
.
Trigonometric: Expand and Use Identity
Evaluate
∫
(
1
−
sin
2
x
)
2
d
x
\displaystyle\int_{ }^{ }\left(1-\sin2x\right)^2dx
∫
(
1
−
sin
2
x
)
2
d
x
Trigonometric Integrals: Cot and Sin
Evaluate
∫
cot
5
x
sin
4
x
d
x
\displaystyle\int\cot^5x\sin^4x \ dx
∫
cot
5
x
sin
4
x
d
x
Trigonometric Integrals: Tangent Only
Evaluate
∫
tan
4
x
d
x
\displaystyle\int\tan^4x \ dx
∫
tan
4
x
d
x
Evaluate the integral
∫
tan
2
x
sec
4
x
d
x
\displaystyle\int\tan^2x\sec^4x\ dx
∫
tan
2
x
sec
4
x
d
x
Fraction with Cot and Sin
Evaluate
∫
cot
4
x
sin
4
x
d
x
\displaystyle\int\frac{\cot^4x}{\sin^4x}dx
∫
sin
4
x
cot
4
x
d
x
Practice: Secant Even
Q:
\textbf{Q:}
Q:
Evaluate
∫
sec
8
x
tan
6
x
d
x
\displaystyle\int\sec^8 x\tan^6 x\ dx
∫
sec
8
x
tan
6
x
d
x
Trigonometric Integrals: Use Identity First
Evaluate
∫
sin
(
15
x
)
cos
(
4
x
)
d
x
\displaystyle\int\sin(15x)\cos(4x) \ dx
∫
sin
(
15
x
)
cos
(
4
x
)
d
x
Practice: Sin and Cos both Even
Q:
\textbf{Q:}
Q:
Evaluate
∫
sin
2
x
cos
2
x
d
x
\displaystyle\int\sin^2x\cos^2x\ dx
∫
sin
2
x
cos
2
x
d
x
Integrals: Trigonometric Functions
Find
∫
3
sin
(
5
x
)
cos
(
5
x
)
cos
(
10
x
)
d
x
\int 3\sin(5x)\cos(5x)\cos(10x) dx
∫
3
sin
(
5
x
)
cos
(
5
x
)
cos
(
10
x
)
d
x
∫
sin
7
x
d
x
\int_{ }^{ }\sin^7xdx
∫
sin
7
x
d
x
Practice Question: Special Trig Integral Using Identities
Practice Question
Find
∫
sin
(
15
x
)
cos
(
4
x
)
d
x
{\displaystyle\int}\sin(15x)\cos(4x)\de{x}
∫
sin
(
15
x
)
cos
(
4
x
)
d
x
.
Practice Question: Trig Integral
Practice Question
Compute
∫
sec
6
x
d
x
{\displaystyle\int}\sec^6x\de{x}
∫
sec
6
x
d
x
.
Practice Question: Trig Integral
Practice Question
Compute
∫
sin
7
x
d
x
{\displaystyle\int}\sin^7x\de{x}
∫
sin
7
x
d
x
.
Practice Question: Trig Integral
Practice Question
Find
∫
cos
4
(
x
)
d
x
{\displaystyle \int}\cos^4(x)\de{x}
∫
cos
4
(
x
)
d
x
.
Trigonometric Intervals
Find
∫
4
sin
3
x
cos
3
x
d
x
\int 4\sin 3x \cos 3x\ dx
∫
4
sin
3
x
cos
3
x
d
x
Evaluate
∫
cot
3
x
csc
3
x
d
x
\int_{ }^{ }\cot^3x\csc^3xdx
∫
cot
3
x
csc
3
x
d
x
Evaluate the integral
∫
tan
2
x
sec
4
x
d
x
\displaystyle\int\tan^2x\sec^4x\ dx
∫
tan
2
x
sec
4
x
d
x
Practice: Sin and Cos both Even
Q:
\textbf{Q:}
Q:
Evaluate
∫
sin
2
x
cos
2
x
d
x
\displaystyle\int\sin^2x\cos^2x\ dx
∫
sin
2
x
cos
2
x
d
x
Practice: Secant Even
Q:
\textbf{Q:}
Q:
Evaluate
∫
sec
8
x
tan
6
x
d
x
\displaystyle\int\sec^8 x\tan^6 x\ dx
∫
sec
8
x
tan
6
x
d
x
Trigonometric: Expand and Use Identity
Evaluate
∫
(
1
−
sin
2
x
)
2
d
x
\displaystyle\int_{ }^{ }\left(1-\sin2x\right)^2dx
∫
(
1
−
sin
2
x
)
2
d
x
Trigonometric Integrals: Cot and Sin
Evaluate
∫
cot
5
x
sin
4
x
d
x
\displaystyle\int\cot^5x\sin^4x \ dx
∫
cot
5
x
sin
4
x
d
x
Trigonometric Integrals: Tangent Only
Evaluate
∫
tan
4
x
d
x
\displaystyle\int\tan^4x \ dx
∫
tan
4
x
d
x
Trigonometric Integrals: Use Identity First
Evaluate
∫
sin
(
15
x
)
cos
(
4
x
)
d
x
\displaystyle\int\sin(15x)\cos(4x) \ dx
∫
sin
(
15
x
)
cos
(
4
x
)
d
x
Fraction with Cot and Sin
Evaluate
∫
cot
4
x
sin
4
x
d
x
\displaystyle\int\frac{\cot^4x}{\sin^4x}dx
∫
sin
4
x
cot
4
x
d
x
Evaluate the integral
∫
sin
4
x
cos
3
x
d
x
\displaystyle\int_{ }^{ }\sin^4x\ \cos^3x\ dx
∫
sin
4
x
cos
3
x
d
x
.
Evaluate the integral
∫
tan
2
x
sec
4
x
d
x
\displaystyle\int_{ }^{ }\tan^2x\sec^4x\ dx
∫
tan
2
x
sec
4
x
d
x
.
Evaluate the integral
∫
sin
4
x
cos
3
x
d
x
\displaystyle\int_{ }^{ }\sin^4x\ \cos^3x\ dx
∫
sin
4
x
cos
3
x
d
x
.