Evaluate : a^2+x^2 d x=x 2 x^2+a^2+a^2 2 (x+x^2+a^2 )+c - Vidyadip

Question

Evaluate : $\int \sqrt{a^2+x^2} \cdot d x=\frac{x}{2} \cdot \sqrt{x^2+a^2}+\frac{a^2}{2} \cdot \log \left(x+\sqrt{x^2+a^2}\right)+c$

✓

Answer

Self

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.(4 Marks)" from Indefinite Integration→Indefinite Integration — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Bismath has half life of 5 days. A sample originally has a mass of $800 \mathrm{mg}$. Find the mass remaining after 30 days.

Find the co-ordinates of the points on the curve $y=x-\frac{4}{x}$, here the tangents are parallel to the line $y=2 x$

The rate of growth of bacteria is proportional to the number present. If initially, there were 1000 bacteria and the number doubles in 1 hour, find the number of bacteria after $2 \frac{1}{2}$ hours. [Take $\sqrt{2}=1.414$ ]

If $a x^2+2 h x y+b y^2=0$, show that $\frac{d^2 y}{d x^2}=0$

Solve the differential equation : $(x+y) \frac{d y}{d x}=1$.

Find the area bounded by the curve $y=-x^2, \mathrm{X}$-axis and lines $x=1$ and $x=4$.

Solve the following differential equations:

$\left(1+2 e^{\frac{x}{y}}\right)+2 e^{\frac{x}{y}}\left(1-\frac{x}{y}\right) \frac{d y}{d x}=0$

Show that lines $\bar{r}=(\hat{i}+\hat{j}-\hat{k})+\lambda(2 \hat{i}-2 \hat{j}+\hat{k})$ and $\bar{r}=(4 \hat{i}-3 \hat{j}+2 \hat{k})+\mu(\hat{i}-2 \hat{j}+2 \hat{k})$ are coplanar. Find the equation of the plane determined by them.

Show that the lines $\frac{x+1}{-10}=\frac{y+3}{-1}=\frac{z-4}{1}$ and $\frac{x+10}{-1}=\frac{y+1}{-3}=\frac{z-1}{4}$ intersect each other.also find the coordinates of the point of intersection

Evaluate the following:

$\int_0^\pi x \cdot \sin x \cdot \cos ^4 x d x$