Question

` int _(0)^(pi//4) sec^(7) theta sin^(3) theta d theta ` is equal to
A. `(1)/(12)`
B. `(3)/(12)`
C. `(5)/(12)`
D. None of these

Answer 1

Correct Answer - C
Let ` l = int _(0)^(pi//4) sec^(7) theta . d theta = int _(0)^(pi//4) (sin^(3) theta )/(cos^(3) theta ) theta d theta `
Put `tan theta = t rArr sec^(2) theta d theta = dt`
` :. l = int _(0)^(1) t^(3) (1+t^(2)) dt = [ (t^(4))/4+ (t^(6))/6 ] _(0)^(1) = 5/12 `