MCQ
$\int_{ - 1}^1 {{{\sin }^3}x{{\cos }^2}x\,dx = } $
  • $0$
  • B
    $1$
  • C
    $\frac{1}{2}$
  • D
    $2$

Answer

Correct option: A.
$0$
a
(a) $\int_{ - 1}^1 {{{\sin }^3}x{{\cos }^2}x\,dx = 0} $,

Since the function is an odd function.

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

Similar questions

The sum to infinity of the following series $\frac{1}{{1.2}} + \frac{1}{{2.3}} + \frac{1}{{3.4}} + ...........$ shall be
The equation of the bisector of the acute angle between the lines $3x - 4y + 7 = 0$ and $12x + 5y - 2 = 0$ is
Let $\alpha $ and $\beta $ are roots of $5{x^2} - 3x - 1 = 0$ , then $\left[ {\left( {\alpha  + \beta } \right)x - \left( {\frac{{{\alpha ^2} + {\beta ^2}}}{2}} \right){x^2} + \left( {\frac{{{\alpha ^3} + {\beta ^3}}}{3}} \right){x^3} -......} \right]$ is
Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{b}=2 \hat{i}+4 \hat{j}-5 \hat{k}$ and $\vec{c}=x \hat{i}+2 \hat{j}+3 \hat{k}, x \in \mathbb{R}$. If $\vec{d}$ is the unit vector in the direction of $\vec{b}+\vec{c}$ such that $\vec{a} \cdot \vec{d}=1$, then $(\vec{a} \times \vec{b}) \cdot \vec{c}$ is equal to
Point $'A'$ lies on the curve $y = {e^{ - {x^2}}}$ and has the coordinate $(x,{e^{ - {x^2}}})$ where $x > 0.$ Point $B$ has the coordinates $(x, 0)$. If $'O'$ is the origin then the maximum area of the triangle $AOB$ is
If $a,\;b,\;c$ are in $A.P.$, $b,\;c,\;d$ are in $G.P.$ and $c,\;d,\;e$ are in $H.P.$, then $a,\;c,\;e$ are in
The sum of the series $3.6 + 4.7 + 5.8 + ........$ upto $(n - 2)$ terms
Let $f(x) =  - 1 + \left| {x - 2} \right|,$ and $g(x) = 1 - \left| x \right|;$ then the set of all points where $\text{fog}$ is discontinuous is
If ${1 \over {x(x + 1)\,(x + 2)....(x + n)}} = {{{A_0}} \over x} + {{{A_1}} \over {x + 1}} + {{{A_2}} \over {x + 2}} + .... + {{{A_n}} \over {x + n}}$ then ${A_r} = $
Jairam purchased a house in Rs. $15000$ and paid Rs. $5000$ at once. Rest money he promised to pay in annual installment of Rs. $1000$ with $10\%$ per annum interest. How much money is to be paid by Jairam $\mathrm{Rs.}$ ...................