Download App

INTEGRALS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsINTEGRALS1 Mark
Question
Evaluate:
$\int\limits^{2\pi}_{0} \cos^{5} \text{x dx}. $
✓

Answer

$\int\limits^{2\pi}_{0} \cos^{5} \text{x dx} = 2 \int\limits^{\pi}_{0} \cos^{5}\text{x dx}$
$\text{and}\ 2\int^\pi_0\cos^5\text{x}\ \text{dx}=0\Rightarrow\int^{2\pi}_0\cos^5\text{x}\ \text{dx}=0$

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 "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

Evaluate the following:
$\tan^{-1}(\tan12)$
→
Prove that $\int_{1}^{3} \frac{d x}{x^{2}(x+1)}=\frac{2}{3}+\log \frac{2}{3}$
→
Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\frac{\text{dy}}{\text{dx}}+\text{e}^\text{y}=0$
→
Consider the identity function IN : N $\rightarrow $ N defined as, IN (x) = x $\forall$ x $\in$ N.
Show that although IN is onto but IN + IN : N $\rightarrow$ N defined as
(IN + IN) (x) = IN (x) + IN (x) = x + x = 2x is not onto.
→
If a line makes angles 90° and 60° respectively with the positive directions of x and y axes, find the angle which it makes with the positive direction of z-axis.
→
If X and Y are 2 × 2 matrices, then solve the following matrix equations for X and Y.
$2\text{X}+3\text{Y}=\begin{bmatrix}2&3\\4&0\end{bmatrix},\ 3\text{X}+2\text{Y}\begin{bmatrix}-2&2\\1&-5\end{bmatrix}$
→
$\int x^{2} e^{x^{3}} d x$ equals
→
A car starts from a point P at time t = 0 seconds and stops at point Q. The distance x, in metres, covered by it, in t seconds is given by
$x=t^{2}\left(2-\frac{t}{3}\right)$
Find the time taken by it to reach Q and also find distance between P and Q.
→
Evaluate the determinant $\left|\begin{array}{cc}x^2-x+1 & x-1 \\ x+1 & x+1\end{array}\right|$
→
Integrate the functions in Exercises:
$\frac{\text{x}}{\text{e}^{\text{x}^2}}$
→