# Math Help - Calculus Question

1. ## Calculus Question

If 0 < k < (pi/2) and the area under the curve y = cos x from x = k to x = (pi/2) is 0.1, then k =

A) 1.471
B) 1.414
C) 1.277
D) 1.120
E) 0.436

2. Originally Posted by frozenflames
If 0 < k < (pi/2) and the area under the curve y = cos x from x = k to x = (pi/2) is 0.1, then k =

A) 1.471
B) 1.414
C) 1.277
D) 1.120
E) 0.436
Thus, the area is,
$\int^{\pi/2}_k\cos x=.1$
Using the fundamental theorem,
$\sin(\pi/2)-\sin k=.1$
Thus,
$1-\sin k=.1$
Thus,
$\sin k=.9$
Using the arc sine we get,
$k\approx 1.12$