Question
Evaluate the integrals:
Answer :
Word Count : 291
_______ _________ ______ _______ ______ _________ ________.
________ ____ ________ __________ ______.
_______ ______ ____ _______ _____ ____ ________ _______ _____ _______ __________.
____ ___ ____ ______ _____ ____ _____ _________ _________ _________ ___.
__________ ____ ________ _________ ________ _________ ________.
_____ ____ ________ ______ ________ __________ ______ _________.
____ _______ ____ _______ ___ ___ __________ _________ _________ ____.
________ __________ ________ _________ ______.
_____ _______ __________ ______ __________ _________ _______.
__________ _____ ___ ______ __________.
_________ __________ ________ __________ __________ ____.
_____ _______ _________ ______ ___ __________ ______ _________ _____ __________.
_______ ________ ______ ________ ______ _________ _____ ______ ____ ______ ___.
________ _______ ____ ________ ______.
_______ __________ ____ __________ ________ __________ _________ ______ ___ _______.
___ ____ __________ ___ ___ ________ ________ _____ __________.
__________ ____ ___ _____ _____ ____ __________ __________.
_________ _______ ________ ___ _________ ________ _________ _________ _______ _______.
_________ ____ ___ ______ ______ _________ _________ ___ _____.
______ __________ ____ _______ ________ ______ ________ __________.
____ ____ ______ ________ _________ ________ _______ ________ _________ ___ _____.
________.
Skip in 10
We are asked to evaluate: [ \int \frac{1}{(x-2)(x^2+4)} , dx ] First, decompose the integrand using partial fractions: [ \frac{1}{(x-2)(x^2+4)} = \frac{A}{x-2} + \frac{Bx + C}{x^2 + 4} ] Multiply through by ((x-2)(x^2+4)): [ 1 = A(x^2 + 4) + (Bx + C)(x-2) ] Expand the right-hand side: [ 1 = A x^2 + 4A + Bx^2 - 2Bx + Cx - 2C ] Combine like terms: [ 1 = (A + B)x^2 + (-2B + C)x + (4A - 2C) ] Equate coefficients with the left-hand side (1 + 0x + 0x^2): 1. Coefficient of (x^2): (A + B = 0 \implies B = -A) 2. Coefficient
_______ ____ ___ ____ _____ __________ _________ ________ _______._______ _________ ______ _______ ______ _________ ________.
________ ____ ________ __________ ______.
_______ ______ ____ _______ _____ ____ ________ _______ _____ _______ __________.
____ ___ ____ ______ _____ ____ _____ _________ _________ _________ ___.
__________ ____ ________ _________ ________ _________ ________.
_____ ____ ________ ______ ________ __________ ______ _________.
____ _______ ____ _______ ___ ___ __________ _________ _________ ____.
________ __________ ________ _________ ______.
_____ _______ __________ ______ __________ _________ _______.
__________ _____ ___ ______ __________.
_________ __________ ________ __________ __________ ____.
_____ _______ _________ ______ ___ __________ ______ _________ _____ __________.
_______ ________ ______ ________ ______ _________ _____ ______ ____ ______ ___.
________ _______ ____ ________ ______.
_______ __________ ____ __________ ________ __________ _________ ______ ___ _______.
___ ____ __________ ___ ___ ________ ________ _____ __________.
__________ ____ ___ _____ _____ ____ __________ __________.
_________ _______ ________ ___ _________ ________ _________ _________ _______ _______.
_________ ____ ___ ______ ______ _________ _________ ___ _____.
______ __________ ____ _______ ________ ______ ________ __________.
____ ____ ______ ________ _________ ________ _______ ________ _________ ___ _____.
________.
IGNOU ACADEMY
Your IGNOU journey, made easier.
- Solved Assignments
- Study Notes
- Guess Papers
- Question Papers
Continue Reading — It's Free
Sign in with Google to unlock more of this answer.
✓ Free access
✓ Unlock up to 60% of the answer
✓ No payment required
✓ Unlock up to 60% of the answer
✓ No payment required
Quick Google sign-in. No separate registration form.