Evaluate the definite integral in Exercise: _ 0 ^ 1 dx 1+x^ 2 - Vidyadip

Question

Evaluate the definite integral in Exercise:$\int\limits_{0}^{1}\frac{\text{dx}}{1+\text{x}^{2}}$

✓

Answer

$\text{Let}\ \text{I}=\int\limits_{0}^{4}\frac{\text{dx}}{1+\text{x}^{2}}$
$\int\frac{\text{dx}}{1+\text{x}^{2}}=\tan^{-1}\text{x}=\text{F}\text{(x)}$ By second fundamental theorem of calculus, we obtain$\text{I}=\text{F}(1)-\text{F}(0)$
$=\tan^{-1}(1)-\tan^{-1}(0)$
$=\frac{\pi}{4}$

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 "2 Marks Questions" from INTEGRALS→INTEGRALS — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

For what value of $\lambda$ are the vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ perpendicular to each other if
$\vec{\text{a}}=2\hat{\text{i}}+3\hat{\text{j}}+4\hat{\text{k}}$ and $\vec{\text{b}}=3\hat{\text{i}}+2\hat{\text{j}}+\lambda\hat{\text{k}}$

Find the values of b for which the function $\text{f}(\text{x})=\sin\text{x}-\text{b}\text{x}+\text{c}$ is a decreasing function on R.

If A = {3, 5, 7} and B = {2, 4, 9} and R is a relation given by "is less than", write R as a set ordered pairs.

Write the value of $\sin^{-1}\Big(\sin\frac{3\pi}{5}\Big)$

Find the area of that parallelogram whose diagonals are denoted by vectors $2 \hat{i}-\hat{j}+5 \hat{k}$ and $3 \hat{i}+\hat{j}+2 \hat{k}$.

Write the principal value of $\sin^{-1}\Big\{\cos\Big(\sin^{-1}\frac{1}{2}\Big)\Big\}$

Write the value of $\cos\Big(2\sin^{-1}\frac{1}{2}\Big).$

Find $\frac { d y } { d x }$ of the function $(\cos x)^y = (\cos y)^x.$

A ordinary cube has four plane faces, one face marked $2$ and another face marked $3,$ find the probability of getting a total of $7$ in $5$ throws.

Write the domain of the real function $\text{f(x)}=\frac{1}{\sqrt{|\text{x}|-\text{x}}}.$