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

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