Write a value of ^ x e^ x dx - Vidyadip

Question

Write a value of $\int\text{a}^{\text{x}}\text{e}^{\text{x}}\text{ dx}$

✓

Answer

Let $\text{I}=\int\text{a}^{\text{x}}\text{e}^{\text{x}}\text{ dx}$$=\int(\text{a}\text{e})^{\text{x}}\text{ dx}$
$=\frac{(\text{a}\text{e})^{\text{x}}}{\log\text{ae}}+\text{C}$
$\therefore\ \text{I}=\frac{(\text{a}\text{e})^{\text{x}}}{\log\text{ae}}+\text{C}$

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→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Write the minimum value of $\text{f}(\text{x})=\text{x}+\frac{1}{\text{x}},\text{x}>0.$

Two cards are drawn from a well shuffled pack of 52 cards, one after another without replacement. Find the probability that one of these is red card and the other a black card?

Find the equation of the line passing through the points (2, -1, 3) and parallel to the line $\vec{\text{r}}=\big(\hat{\text{i}}-2\hat{\text{j}}+\hat{\text{k}}\big)+\lambda\big(2\hat{\text{i}}+3\hat{\text{j}}-5\hat{\text{k}}\big).$

If $\vec{\text{a}},\vec{\text{b}},\vec{\text{c}}$ represent the sides of a triangle taken in order, then write the value of $\vec{\text{a}}+\vec{\text{b}}+\vec{\text{c}}$.

If $\text{P(A)}=\frac{6}{11},\text{P(B)}=\frac{5}{11}$ and $\text{P}(\text{A}\cap\text{B})=\frac{7}{11},$ find
$\text{P}(\text{A}\cap\text{B})$

Find the rate of change of the volume of a sphere with respect to its surface area when the radius is 2cm.

The cooperative stores of a particular school has 10 dozen physics books, 8 dozen chemistry books and 5 dozen mathematics books. Their selling prices are Rs. 8.30, Rs. 3.45 and Rs. 4.50 each respectively. Find the total amount the store will receive from selling all the items.

Define vector product of two vectors.

Find the values of 'a' for which the vectors
$\vec{\text{a}}=\hat{\text{i}}+2\hat{\text{j}}+\hat{\text{k}},\vec\beta={\text{a}}\hat{\text{i}}+\hat{\text{j}}+2\hat{\text{k}}$ and $\vec\gamma=\hat{\text{i}}+2\hat{\text{j}}+\text{a}\hat{\text{k}}$ are coplanar.

Differentiate $a^x w.r.t. x,$ where a is a positive constant.