#4 Evaluate the Integral | University of Cambridge - Edubirdie

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

2023
Views:

437

Pages:

2
Author:

Shahbaz A.

Integration shahbaz ahmed August 2024 Relevant concepts and formulas limn−→∞ (1 + n1 )n = e Putting x= 1 n When n −→ ∞ =⇒ x → 0 Also x= 1 n =⇒ n = 1 x When x → 0 =⇒ n → ∞ So 1 limx→0 (1 + x) x = e Where e is an irrational number such that 2 < e < 3 Also loge x = ln x 1 d dx (ln x) R 1 x = 1 x dx = ln |x| + C ......................................... Evaluate the integral Z cos x ln sin x sin x ln sin x sin x dx Solution Z cos x d dx (ln sin x) = d dx (ln sin x) dx 1 d sin x dx (sin x) = d(ln sin x) = 1 sin x 1 sin x cos x cos x dx Putting in equation (1) Z cos x ln sin x sin x Z cos x ln sin x sin x Z dx = ln sin x d[ln sin x] 1 dx = [ln sin x]2 + C 2 2 (1)

Related Documents

#4 Evaluate the Integral

#4 Evaluate the Integral - Page 1

#4 Evaluate the Integral - 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