MCQ
$\int_{\,\pi }^{\,10\pi } {\,|\sin x|dx} $ is
- A$20$
- B$8$
- C$10$
- ✓$18$
✓
Answer
Correct option: D.
$18$
d
(d) $\int_\pi ^{10\pi } {|\sin x|dx = \int_0^\pi {|\sin x|dx + \int_\pi ^{10\pi } {\,\,|\sin x|dx} } } - \int_0^\pi {\,|\sin x|dx} $
(d) $\int_\pi ^{10\pi } {|\sin x|dx = \int_0^\pi {|\sin x|dx + \int_\pi ^{10\pi } {\,\,|\sin x|dx} } } - \int_0^\pi {\,|\sin x|dx} $
$ = \int_0^{10\pi } {|\sin x|dx - \int_0^\pi {\,|\sin x|dx} } $
$ = 10\int_{\,0}^{\,\pi } {|\sin x|dx - \int_{\,0}^{\,\pi } {\,|\sin x|dx} } $
$ = 9\int_{\,0}^{\,\pi } {\sin x\,dx} $
$[\because \,|\sin x|$ is periodic with period $\pi $ and in $[0,\pi ],\sin x \ge 0]$
$ = 9\,[ - \cos x]_0^\pi = 9\,( - \cos \pi + \cos 0)$
$ = 9\,(1 + 1) = 18$.
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
The function ${1 \over {1 + {x^2}}}$ is decreasing in the interval
→The distance between the planes $2x + 2y - z +2 = 0$ and $4x + 4y - 2z + 5 = 0$ is:
→If matrix $A = \left[ {\begin{array}{*{20}{c}}1&{ - 1}\\1&1\end{array}} \right],$ then
→Integrating factor of the differential equation $\frac{d y}{d x}+y \tan x-\sec x=0$ is
→If $(x^2 + y^2) dy = xy \ dx, y(1) = 1$, and $y(x_0) = e$, then $x_0 =$
→The number of arbitrary constants in the particular solution of a differential equation of second order is $($are$):$
→$\int_{}^{} {\frac{{10{x^9} + {{10}^x}{{\log }_e}10}}{{{{10}^x} + {x^{10}}}}} \;dx = $
→Consider the circuit,If the probability that each switch is closed is $p$, then find the probability of current flowing through $AB$
→the order of the single matrix obtained from
$\left[\begin{array}{cc}1 & -1 \\ 0 & 2 \\ 2 & 3\end{array}\right]_{3 \times 2}\left\{\left[\begin{array}{ccc}-1 & 0 & 2 \\ 2 & 0 & 1\end{array}\right]_{2 \times 3}-\left[\begin{array}{lll}0 & 1 & 23 \\ 1 & 0 & 21\end{array}\right]_{2 \times 3}\right\}$ is
→$\left[\begin{array}{cc}1 & -1 \\ 0 & 2 \\ 2 & 3\end{array}\right]_{3 \times 2}\left\{\left[\begin{array}{ccc}-1 & 0 & 2 \\ 2 & 0 & 1\end{array}\right]_{2 \times 3}-\left[\begin{array}{lll}0 & 1 & 23 \\ 1 & 0 & 21\end{array}\right]_{2 \times 3}\right\}$ is
Let the slope of the tangent to a curve $y=f(x)$ at $(x, y)$ be given by $2 \tan x(\cos x-y)$. if the curve passes through the point $(\frac{\pi}{4},0)$, then the value of $\int \limits_{0}^{\pi / 2} y d x$ is equal to
→