Integrate the function in Exercise: x ^2x - Vidyadip

Question

Integrate the function in Exercise:
$\text{x} \ \sec^2\text{x}$

✓

Answer

Let $\text{I}=\int\text{x}\sec^2\text{x dx}$
Taking x as first function and $sec^2x$ as second function and integrating by parts, we obtain.
$\text{I}=\text{x}\int\sec^2\text{x dx}-\int\Big[\Big\{\frac{\text{d}}{\text{dx}}\text{x}\int\sec^2\text{x} \ \text{dx}\Big\}\text{dx}\Big]$
$=\text{x}\tan\text{x}-\int1.\tan\text{x dx}$
$=\text{x}\tan\text{x}+\text{log}|\cos\text{x}|+\text{C}$

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 "2 Marks Questions" 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

When three dice are thrown, write the probability of getting 4 or 5 on each of the dice simultaneously.

Which of the following distributions of a random variable X are the probability distributions?

X:	3	2	1	0	-1
P(X):	0.3	0.2	0.4	0.1	0.05

Find the area bounded by the curve $y=x^3-6 x^2+$ $8 x, x=a, x=b$ and the $x$-axis.

Write the cartesian and vector equations of x-axis.

If $-\frac{\pi}{2}<\text{x}<0\text{ and y}=\tan^{-1}\sqrt{\frac{1-\cos2\text{x}}{1+\cos2\text{x}}},$ find $\frac{\text{dy}}{\text{dx}}.$

Evaluate the definite integral $\int_{4}^{5} e^{x} d x$

If A = $\left[\begin{array}{lll} {1} & {3} & {3} \\ {1} & {4} & {3} \\ {1} & {3} & {4} \end{array}\right]$then verify that $A$ adj $A = | A|\ I$. Also find $A^{–1}.$

Find the area bounded by the curve y = cos x between x = 0 and x = 2$\pi$

Construct a $2 \times 3$ matrix $A = [a_{ij}]$ whose elements $a_{ij}$ are give by:$\text{a}_\text{ij}=\frac{(\text{i}+\text{j})^2}{2}$

If $\text{A}=\begin{bmatrix}2&4\\4&3\end{bmatrix},\text{X}=\begin{bmatrix}\text{n}\\1\end{bmatrix},\text{B}=\begin{bmatrix}8\\11\end{bmatrix}$and AX = B, then find n.