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" 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

Find the direction cosines of the line passing through the two points (-2, 4, -5) and (1, 2, 3).

If A is a square matrix such that A (adj A) = 5I, where I denotes the identity matrix of the same order. Then, find the value of |A|.

A random variable X has the following probability distribution:

Values of X:	0	1	2	3	4	5	6	7	8
P(X)	a	3a	5a	7a	9a	11a	13a	15a	17a

Determine:

The Value of a.

Show that $\text{f}(\text{x})=\text{x}+\cos\text{x}-\text{a}$ is an increasing function on R for all values of a.

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
$\text{P}(\text{A}\cap\text{B})$

For any three vectors $\vec{\text{a}},\vec{\text{b}}$ and $\vec{\text{c}}$ write the value of $\vec{\text{a}}\times\big(\vec{\text{b}}+\vec{\text{c}}\big)+\vec{\text{b}}\times\big(\vec{\text{c}}+\vec{\text{a}}\big)+\vec{\text{c}}\times\big(\vec{\text{a}}+\vec{\text{b}}\big).$

Construct a 3 × 4 matrix, whose elements are given by:

$\text{a}_{\text{ij}}=\frac{1}{2} \left|-3{\text{i}+\text{j}}\right| $

Find the values of x, y and z from the following equations:
$\begin{bmatrix}\text{x + y+ z}\\ \text{x + z}\\\ \text{y + z} \end{bmatrix}=\begin{bmatrix}9\\5\\7\end{bmatrix} $

If $\frac{\pi}{2}\leq\text{x}\leq\frac{3\pi}{2}$ and $\text{y}=\sin^{-1}(\sin\text{x}),$ find $\frac{\text{dy}}{\text{dx}}.$

By using the properties of definite integral, evaluate the integral in Exercise:
$\int\limits_{0}^{\frac{\pi}{2}}\cos^{2}\text{x}\ \text{dx}$