Question

Area of the figure bounded by the interval $[-\frac{5\pi }{6},\pi ]$ of the $x$-axis, the graph of the function $y=$ cosx and the segments of the straight lines $x=-\frac{5\pi }{6}$ and $x=\pi$ is

• A. 7/2
• B. 5/2
• C. 3/4
• D. 3/2

Answer 1

The correct option is A 7/2

$|{\int }_{-\frac{5\pi }{6}}^{\frac{-\pi }{2}}cosx.dx|+|{\int }_{-\frac{\pi }{2}}^{0}cos\left(x\right).dx|+{\int }_0^{\frac{\pi }{2}}cos\left(x\right).dx+|{\int }_{\frac{\pi }{2}}^{\pi }cos\left(x\right).dx|$
$=|\left[sin\right(x){]}_{-\frac{5\pi }{6}}^{\frac{-\pi }{2}}|+|[sin\left(x\right){]}_{-\frac{\pi }{2}}^0|+\left[sin\right(x){]}_0^{\frac{\pi }{2}}+|[sin\left(x\right){]}_{\frac{\pi }{2}}^{\pi }|$
$=|-1+\frac{1}{2}|+1+1+|-1|$
$=\frac{1}{2}+2+1$
$=\frac{7}{2}$ sq units.