If I1 = ∫10e−xcos2x dx; I2 = ∫10e−x2cos2x dx and I3 = ∫10e−x3dx; then

The correct option is D I3>I2>I1
Given:
I1 = ∫10e−xcos2x dx; I2 = ∫10e−x2cos2x dx and I3 = ∫10e−x3dx
For x∈(0,1), x > x2 ⇒ −x < −x2 ⇒ x2 > x3 ⇒ −x2 < −x3 ⇒ e−x2 < e−x3 and e−x < e−x2 ⇒ e−x < e−x2 < e−x3 ⇒ e−x3 > e−x2 > e−x ⇒ I3 > I2 > I1
Green line denotes f(x) = e−xcos2x
Blue line denotes g(x) = e−x2cos2x
Red line denotes h(x) = e−x3
Also, from the graph we get the same result.
Hence, option D is correct.