Evaluate _0^1 d x 1+x^2 . - Vidyadip

Question

Evaluate $\int_0^1 \frac{d x}{1+x^2}$.

✓

Answer

$\int_0^1 \frac{d x}{1+x^2}=\left(\tan ^{-1} x\right)_0^1$
$=\tan ^{-1} 1-\tan ^{-1} 0=\frac{\pi}{4}-0=\frac{\pi}{4}$

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 "1 Marks Question" 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

$\int \sqrt{x^{2}-8 x+7} d x$ is equal to

Evaluate the determinant $\left|\begin{array}{cc} {\cos \theta} & {-\sin \theta} \\ {\sin \theta} & {\cos \theta} \end{array}\right|$

Find the sum of the order and degree of the differential equation $\text{y}=\text{x}\Big(\frac{\text{dy}}{\text{dx}}\Big)^{3}+\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}.$

The total cost $C(x)$ in Rupees, associated with the production of x units of an item is given by $C(x) = 0.005x^3 - 0.02x^2 + 30x + 5000.$
Find the marginal cost when 3 units are produced, where by marginal cost we mean the instantaneous rate of change of total cost at any level of output.

If $\left[\begin{array}{cc}\lambda-4 & -3 \\ 1 & 6-\lambda\end{array}\right]=\left[\begin{array}{ll}a & -3 \\ 1 & -4\end{array}\right]$, then find the value of $a$.

Evaluate the definite integral $\int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{\sin x+\cos x}{\sqrt{\sin 2 x}} d x$

$\text{If}\overrightarrow{\text{a}} = \hat{\text{i}} + 2\hat{\text{j}} - \hat{\text{k}},$ $\overrightarrow{\text{b}} =2\hat{\text{i}} + \hat{\text{j}} + \hat{\text{k}}$ and $ \overrightarrow{\text{c}} = 5\hat{\text{i}} + 4\hat{\text{j}} - 3\hat{\text{k}},$ then find the value of $(\overrightarrow{\text{a}}+\overrightarrow{\text{b}}).\overrightarrow{\text{c.}}$

Evaluate: $\int\text{(1-x)}\sqrt{x}\text{dx}.$

Classify the 40-watt measure as scalar and vector.

Consider two points P and Q with position vectors $\vec{OP}=3 \vec{a}-2 \vec{b}$ and $\vec{OQ}=\vec{a}+\vec{b}$. Find the position vector (internally) of a point R which divides the line joining P and Q in the ratio 2 : 1.