Question

$LaTeX: \text{Suppose that } f \text{ is a function such that } f'' \text{ is continuous. Further suppose that } $ $Suppose\; that$ f  is a function such that  f ″  is continuous. Further suppose that 

$LaTeX: \displaystyle\int_0^{\pi/2}f(x)\cos(x)dx=-2 \text{ and } \displaystyle\int_0^{\pi/2}f(x)\sin(x)dx=3.$ $\int$ 0 π / 2 f ( x ) cos ⁡ ( x ) d x = − 2  and  ∫ 0 π / 2 f ( x ) sin ⁡ ( x ) d x = 3. 
 

$LaTeX: \text{Using the values in the table below, evaluate the integral }\displaystyle\int_0^{\pi/2}f'(x)\sin(x)dx.$ $Using\; the\; values\; in\; the\; table\; below,\; evaluate\; the\; integral$ ∫ 0 π / 2 f ′ ( x ) sin ⁡ ( x ) d x . 

  

A) $3$ 

B) $7$ 

C) $-$ 1

D) $-$ 2 

E) $-$ 5 

F) 

$5$