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12

Integration by Trigonometric Substitution

Lecture no. 12 from the course: Understanding Calculus II: Problems, Solutions, and Tips

Integration by Trigonometric Substitution

Taught by Professor Bruce H. Edwards | 31 min | Categories: The Great Courses Plus Online Mathematics Courses

Trigonometric substitution is a technique for converting integrands to trigonometric integrals. Evaluate several cases, discovering that you can conveniently represent these substitutions by right triangles. Also, what do you do if the solution you get by hand doesn’t match the calculator’s answer?

36 Lectures

1
Image of Basic Functions of Calculus and Limits
Basic Functions of Calculus and Limits
0 of 32 min
2
Image of Differentiation Warm-up
Differentiation Warm-up
0 of 30 min
3
Image of Integration Warm-up
Integration Warm-up
0 of 30 min
4
Image of Differential Equations—Growth and Decay
Differential Equations—Growth and Decay
0 of 31 min
5
Image of Applications of Differential Equations
Applications of Differential Equations
0 of 30 min
6
Image of Linear Differential Equations
Linear Differential Equations
0 of 30 min
7
Image of Areas and Volumes
Areas and Volumes
0 of 30 min
8
Image of Arc Length, Surface Area, and Work
Arc Length, Surface Area, and Work
0 of 29 min
9
Image of Moments, Centers of Mass, and Centroids
Moments, Centers of Mass, and Centroids
0 of 30 min
10
Image of Integration by Parts
Integration by Parts
0 of 30 min
11
Image of Trigonometric Integrals
Trigonometric Integrals
0 of 31 min
12
Image of Integration by Trigonometric Substitution
Integration by Trigonometric Substitution
0 of 31 min
13
Image of Integration by Partial Fractions
Integration by Partial Fractions
0 of 31 min
14
Image of Indeterminate Forms and L'Hôpital's Rule
Indeterminate Forms and L'Hôpital's Rule
0 of 31 min
15
Image of Improper Integrals
Improper Integrals
0 of 31 min
16
Image of Sequences and Limits
Sequences and Limits
0 of 30 min
17
Image of Infinite Series—Geometric Series
Infinite Series—Geometric Series
0 of 31 min
18
Image of Series, Divergence, and the Cantor Set
Series, Divergence, and the Cantor Set
0 of 32 min
19
Image of Integral Test—Harmonic Series, p-Series
Integral Test—Harmonic Series, p-Series
0 of 30 min
20
Image of The Comparison Tests
The Comparison Tests
0 of 31 min
21
Image of Alternating Series
Alternating Series
0 of 31 min
22
Image of The Ratio and Root Tests
The Ratio and Root Tests
0 of 31 min
23
Image of Taylor Polynomials and Approximations
Taylor Polynomials and Approximations
0 of 31 min
24
Image of Power Series and Intervals of Convergence
Power Series and Intervals of Convergence
0 of 30 min
25
Image of Representation of Functions by Power Series
Representation of Functions by Power Series
0 of 30 min
26
Image of Taylor and Maclaurin Series
Taylor and Maclaurin Series
0 of 32 min
27
Image of Parabolas, Ellipses, and Hyperbolas
Parabolas, Ellipses, and Hyperbolas
0 of 29 min
28
Image of Parametric Equations and the Cycloid
Parametric Equations and the Cycloid
0 of 30 min
29
Image of Polar Coordinates and the Cardioid
Polar Coordinates and the Cardioid
0 of 30 min
30
Image of Area and Arc Length in Polar Coordinates
Area and Arc Length in Polar Coordinates
0 of 32 min
31
Image of Vectors in the Plane
Vectors in the Plane
0 of 30 min
32
Image of The Dot Product of Two Vectors
The Dot Product of Two Vectors
0 of 31 min
33
Image of Vector-Valued Functions
Vector-Valued Functions
0 of 30 min
34
Image of Velocity and Acceleration
Velocity and Acceleration
0 of 30 min
35
Image of Acceleration's Tangent and Normal Vectors
Acceleration's Tangent and Normal Vectors
0 of 30 min
36
Image of Curvature and the Maximum Bend of a Curve
Curvature and the Maximum Bend of a Curve
0 of 31 min

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