_ ,0 ^ , ^3 x ,dx = - Vidyadip

MCQ

$\int_{\,0}^{\,\pi } {{{\cos }^3}x\,dx = } $

A
$ - 1$
✓
$0$
C
$1$
D
$\pi $

✓

Answer

Correct option: B.

$0$

b
(b) $\int_0^\pi {{{\cos }^3}xdx = \int_0^{2.\frac{\pi }{2}} {{{\cos }^3}x\,dx = 0} } $,

$\{\because \,\,{{\cos }^{3}}(\pi -x)=-{{\cos }^{3}}x\}$ .

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

More "M.C.Q (1 Marks)" from 7.2 definite integral→7.2 definite integral — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $A = \left[ {\begin{array}{*{20}{c}}0&1\\0&0\end{array}} \right],I$ is the unit matrix of order $2$ and $a, b$ are arbitrary constants, then ${(aI + bA)^2}$ is equal to

Let $A = \left[ {\begin{array}{*{20}{c}}5&{5\alpha }&\alpha \\0&\alpha &{5\alpha }\\0&0&5\end{array}} \right]$, If ${\left| A \right|^2} = 25$, then $\left| \alpha \right|$ equals

Let $[x]$ be the greatest integer less than or equals to $x$. Then, at which of the following point($s$) the function $f(x)=x \cos (\pi(x+[x]))$ is discontinuous?

$[A]$ $x=-1$ $[B]$ $x=0$ $[C]$ $x=2$ $[D] x=1$

If $\smallint f\left( x \right)\;dx = \varphi \left( x \right)$, then $\smallint {x^5}\;f\left( {{x^3}} \right)\;dx = $

If $A = \left( {\begin{array}{*{20}{c}}1&2&0\\0&1&2\\2&0&1\end{array}} \right),$then $adj \,A$

The solution of $({\rm{cosec}}\,x\log y)dy + ({x^2}y)dx = 0$ is

If $\text{f(x)}=\text{x}\sin\frac{1}{\text{x}},\text{ x}\neq0,$ then the value of the function at x = 0, so that the function is continuous at x = 0, is:

0
-1
1
indeterminate

In which of the following graphs $x = c$ is the point of inflection .

If the curve, $y = y ( x )$ represented by the solution of the differential equation $\left(2 x y^{2}-y\right) d x+x d y=0,$ passes through the intersection of the lines, $2 x -3 y =1$ and $3 x+2 y=8,$ then $|y(1)|$ is equal to ...... .

If vectors $\vec A = 2i + 3j + 4k$, $\vec B = i + j + 5k$, and $\vec C$ form a left handed system, then $\vec C$ is