∫ex1 + sinx1 + cosxdx is equal to
ex + C
extanx2 + C
exsinx + C
tanx2 + C
∫- π4π4dx1 + cos2x is equal to
4
2
0
1
D.
Let I = ∫- π4π4dx1 + cos2x = ∫- π4π4dx2 cos2x = 12 ∫- π4π4sec2xdxLet fx = sec2x⇒ f- x = sec2- x = sec2x = fxHence, f(x) is an even function∴ I = 22∫0π4sec2xdx = tanx0π4 = tanπ4 - tan0 = 1 - 0 = 1