Evaluate the following integrals: ^1_01 1+x^2 dx - Vidyadip

Question

Evaluate the following integrals:$\int\limits^1_0\frac{1}{1+\text{x}^2}\text{ dx}$

✓

Answer

$\int\limits^1_0\frac{1}{1+\text{x}^2}\text{ dx}$$=\big[\tan^{-1}\text{x}\big]^1_0$
$=\tan^{-1}1-\tan^{-1}0$
$=\frac{\pi}{4}-0$
$=\frac{\pi}{4}$

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 "Solve the Following Question.(2 Marks)" from Definite Integrals→Definite Integrals — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Differentiate the following w.r.t. x :

$\sqrt{x^2+4 x-7}$

If $\text{A}=\begin{bmatrix}1&-3&2\\2&0&2\end{bmatrix}$ and $\text{B}=\begin{bmatrix}2&-1&-1\\1&0&-1\end{bmatrix},$ find the matrix C such that A + B + C is zeor matrix.

If a vector makes angles $\alpha,\beta,\gamma$ with OX, OY and OZ respectively. then write the value of $\sin^2\alpha+\sin^2\beta+\sin^2\gamma$.

Find the principal value of the following:
$\cos^{-1}\Big(-\frac{1}{\sqrt2}\Big)$

If $A=\{2,3,4,5,6\}$, then which of the following is 'not' true ?

Evaluate the following integrals:
$\int\frac{\sin^3\text{x}-\cos^3\text{x}}{\sin^2\text{x}\cos^2\text{x}}\text{dx}$

Determine the order and degree of the following differential equations. state also whether they are linear or non linear.
$\sqrt{1+\Big(\frac{\text{dy}}{\text{dx}}\Big)^2}=\Big(\text{c}\frac{\text{d}^2\text{y}}{\text{dx}^2}\Big)^{\frac{1}{3}}$

If $\begin{bmatrix}1&0&0\\0&-1&0\\0&0&-1\end{bmatrix}\begin{bmatrix}\text{x}\\\text{y}\\\text{z}\end{bmatrix}=\begin{bmatrix}1\\0\\1\end{bmatrix}$, find x, y and z.

Obtain the differential equation by eliminating the arbitrary constants from the following equations:

$A x^2+B y^2=1$

Write $A^{-1}$ for $\text{A}=\begin{bmatrix} 2 & 5 \\ 1 & 3 \end{bmatrix}$