Integration Notes | University of Cambridge - Edubirdie

University:
University of Cambridge
Course:
0580 IGCSE | Mathematics
Academic year:

2023
Views:

372

Pages:

2
Author:

Shahbaz A.

integration shahbaz ahmed August 2024 Relevant formula d −1 dx (tan x) = 1 1+x2 1 d(tan−1 x) = 1+x 2 dx R 1 R d(tan−1 x) = 1+x 2 dx R 1 tan−1 x = 1+x 2 dx Or R 1 1+x2 dx = tan−1 x Evaluate the integral Z sin θ dθ 1 + cos2 θ Z sin θ dθ 1 + cos2 θ Solution 1 (1) Let x = cos θ dx dθ = d dθ (cos θ) dx dθ = − sin θ dx = − sin θ dθ Or −dx = sin θ dθ Putting the values of x = cos θ and −dx = sin θ dθ in equation (4) Z sin θ dθ = − 1 + cos2 θ Z dx = − tan−1 x + C 2 1+x Putting x = cos θ Z sin θ dθ = − tan−1 (cos θ) + C 2 1 + cos θ 2

Related Documents

Integration Notes

Integration Notes - Page 1

Integration Notes - Page 2

of 2

Recommended Documents

Laplace Transform x cos (ax)

Laplace Transform x cos (ax)

University of Cambridge 0580 IGCSE | Mathematics

Answer Key

Q3 Cambridge International AS and A Level

Q3 Cambridge International AS and A Level

University of Cambridge 0580 IGCSE | Mathematics

Answer Key

New Documents from this Course

Laplace Transform of xsin(ax)+cos(ax)

Laplace Transform of xsin(ax)+cos(ax)

University of Cambridge 0580 IGCSE | Mathematics

Answer Key

Laplace Transform of xsin(ax)+xcos(ax)

Laplace Transform of xsin(ax)+xcos(ax)

University of Cambridge 0580 IGCSE | Mathematics

Answer Key

Laplace Transform of sin(ax)+xcos(ax)

Laplace Transform of sin(ax)+xcos(ax)

University of Cambridge 0580 IGCSE | Mathematics

Answer Key

Laplace Transform of e^(bx) sin(ax)+e^(bx) cos(ax)

Laplace Transform of e^(bx) sin(ax)+e^(bx) cos(ax)

University of Cambridge 0580 IGCSE | Mathematics

Answer Key

Laplace Transform of e^(bx) cos(ax)

Laplace Transform of e^(bx) cos(ax)

University of Cambridge 0580 IGCSE | Mathematics

Answer Key

Laplace Transform of e^(bx) sin(ax)

Laplace Transform of e^(bx) sin(ax)

University of Cambridge 0580 IGCSE | Mathematics

Answer Key

Laplace Transform cos(ax)

Laplace Transform cos(ax)

University of Cambridge 0580 IGCSE | Mathematics

Answer Key

Integral Formula of Product Functions

Integral Formula of Product Functions

University of Cambridge 0580 IGCSE | Mathematics

Answer Key

First Order Differential Equations Initial Value Problems

First Order Differential Equations Initial Value Problems

University of Cambridge 0580 IGCSE | Mathematics

Answer Key

Cambridge International Examination 9709/21

Cambridge International Examination 9709/21

University of Cambridge 0580 IGCSE | Mathematics

Answer Key

Cambridge International Advanced Subsidiary May-June 2015

Cambridge International Advanced Subsidiary May-June 2015

University of Cambridge 0580 IGCSE | Mathematics

Answer Key

Trigonometric Limit Theorem: Applications in Calculations

Trigonometric Limit Theorem: Applications in Calculations

University of Cambridge 0580 IGCSE | Mathematics

Assignment