Download App

INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS1 Mark
MCQ
Choose the correct answer in Exercise: The value of $\int^{\frac{\pi}{2}}\limits_{\frac{-\pi}{2}}\text{(x}^{3}+\text{x}\cos\text{x}+\tan^{5}\text{x}+1)\text{dx}\ $is
  • A
    0
  • B
    2
  • ✓
    $\pi$
  • D
    1
✓

Answer

Correct option: C.
$\pi$
$\text{Let}\ \text{I}=\int^{\frac{\pi}{2}}\limits_{\frac{-\pi}{2}}\text{(x}^{3}+\text{x}\cos\text{x}+\tan^{5}\text{x}+1)\text{dx}=\int^{\frac{\pi}{2}}\limits_{\frac{-\pi}{2}}\text{x}^{3}\text{dx}+\int^{\frac{\pi}{2}}\limits_{\frac{-\pi}{2}}\text{x}\cos\text{x}\ \text{dx}+\int^{\frac{\pi}{2}}\limits_{\frac{-\pi}{2}}\tan^{5}\text{x}\ \text{dx}+\int^{\frac{\pi}{2}}\limits_{\frac{-\pi}{2}}1\text{dx}$
$\Rightarrow\ \ \text{I}=0+0+0+\text{(x)}^{\frac{\pi}{2}}_{\frac{-\pi}{2}}=\bigg(\frac{-\pi}{2}\bigg)=\pi$

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 INTEGRALS→INTEGRALS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

$\mathop {Lim}\limits_{\lambda  \to 0} \,\,{\left( {\int\limits_0^1 {{{(1 + x)}^\lambda }dx} } \right)^{\frac{1}{\lambda }}}$ is equal to
→
$z = 10x + 25y$ subject to $0\leq\text{X}\leq3$ and $0\leq\text{X}\leq3,$ $\text{x}+\text{y}\leq5$ then the maximum value of $z$ is:
→
A fair coin is tossed a fixed number of times. If the probability of getting seven heads is equal to that of getting nine heads, the probability of getting two heads is:
→
The solution of $y{e^{ - x/y}}dx - (x{e^{ - x/y}} + {y^3})dy = 0$ is
→
For which of the following elements in the determinant $\triangle\begin{bmatrix}2&8\\4&7\end{bmatrix},$ the minor of the element is $2 :$
→
If $y = a\sin x + b\cos x,$ then ${y^2} + {\left( {{{dy} \over {dx}}} \right)^2}$ is a
→
If $a = i + j + k,\,\,b = 4i + 3j + 4k$ and $c = i + \alpha j + \beta k$ are linearly dependent vectors and $|c| = \sqrt 3 ,$ then
→
If $A, B$ are non-singular square matrices of the same order, then $\left(A B^{-1}\right)^{-1}=$
→
If a metallic circular plate of radius $50\, cm$ is heated so that its radius increases at the rate of $1\, mm$ per hour, then the rate at which, the area of the plate increases (in $cm^2/hour$) is
→
Let $f: R \rightarrow R$ be a function defined by $f(x)=\max \left\{x, x^{2}\right\} .$ Let $S$ denote the set of all points in $R ,$ where $f$ is not differentiable. Then
→