Grade 12Integral Calculus
Integrate the following and please simplify it. 1 / (a^2sin^2x + b^2cos^2x)
1 Answer
Arun
∫ 1/(a²cos²x + b²sin²x) dx
= ∫ sec²x/(a² + b²tan²x) dx [dividing up and down by cos²x]
put btanx = u and sec²x dx = du/b. the integral becomes
(1/b) ∫ du/(a² + u²)
= (1/b) [(1/a) tanֿ¹(u/a)]
= ∫ sec²x/(a² + b²tan²x) dx [dividing up and down by cos²x]
put btanx = u and sec²x dx = du/b. the integral becomes
(1/b) ∫ du/(a² + u²)
= (1/b) [(1/a) tanֿ¹(u/a)]
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