Download App

STD 12 - 7.2 definite integral — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 7.2 definite integral4 Marks
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} $

$ = \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.

Start Generating Free

Explore more

JEE STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If the shortest distance between the lines $\frac{\mathrm{x}-\lambda}{2}=\frac{\mathrm{y}-4}{3}=\frac{\mathrm{z}-3}{4}$ and $\frac{x-2}{4}=\frac{y-4}{6}=\frac{z-7}{8}$ is $\frac{13}{\sqrt{29}}$, then a value of $\lambda$ is $:$
→
The corner points of the bounded feasible region are $(0,1),(0,7),(2,7),(6,3)(6,0)(1,0)$ For the objective function $\mathrm{Z}=3 x-y$

$(i)$ At which point, $Z$ is minimum?

$(ii)$ At which point, $Z$ is maximum ?

$(iii)$ The maximum value of $\mathrm{Z}$ is $\ldots \ldots \ldots$

$(iv)$ The minimum value of $\mathrm{Z}$ is $\ldots \ldots \ldots$

→
If A denotes the sum of all the coefficients in the expansion of $\left(1-3 x+10 x^2\right)^n$ and $B$ denotes the sum of all the coefficients in the expansion of $\left(1+x^2\right)^{ n }$, then :
→
A conic passes through the point $(2, 4)$  and is such that the segment of any of its tangents at any point contained between the co-ordinate axes is bisected at the point of tangency. Then the foci of the conic are :
→
${d \over {dx}}\left( {{x^3}{{\tan }^2}{x \over 2}} \right)=$
→
The solution of $dy = \cos x(2 - y\cos {\rm{ec}}x)dx$ where $y = 2$ when $x = \frac{\pi }{2}$ is
→
In a $\triangle A B C$, points $X$ and $Y$ are on $A B$ and $A C$, respectively, such that $X Y$ is parallel to $B C$. Which of the two following equalities always hold? (Here $[P Q R]$ denotes the area of $\triangle P Q R)$.

$I$. $[B C X]=[B C Y]$

$II$. $[A C X] \cdot[A B Y]=[A X Y] \cdot[A B C]$

→
Greatest value of the function, $f(x) =  - 1 + \frac{2}{{{2^x}^2 + 1}}$ is 
→
Let $a_1, a_2, a_3, ……$ be and $A.P$ with $a_6 = 2.$ Then the common difference of this $A.P.,$ which maximizes the product $a_1a_4a_5$ is
→
If $\omega $ is a complex cube root of unity, then for positive integral value of$n$, the product of $\omega .{\omega ^2}.{\omega ^3}........{\omega ^n}$, will be
→