Write a value of ^ ax a f(x)+f'(x) dx - Vidyadip

Question

Write a value of $\int\text{e}^{\text{ax}}\{\text{a }\text{f(x)}+\text{f}'(\text{x})\}\text{ dx}$

✓

Answer

Let $\text{I}=\int\text{e}^{\text{ax}}\{\text{a }\text{f(x)}+\text{f}'(\text{x})\}\text{ dx}$
We know that,
$\int\text{e}^{\text{ax}}\{\text{a }\text{f(x)}+\text{f}'(\text{x})\}\text{ dx}=\text{e}^{\text{ax}}\text{f(x)}+\text{C}$
Which is a general formula.

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 Indefinite Integrals→Indefinite 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 a unit vector perpendicular to vectors $(\vec{a}+\vec{b})$ and $(\vec{a}-\vec{b})$, when $\vec{a}=2 \hat{i}+\hat{j}-2 \hat{k}, \vec{b}=\hat{i}-2 \hat{j}+2 \hat{k}$

In each of the verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
$\text{x + y} = \text{tan}^{–1}\ \text{y} \ \ :\ \text{y}^2 \text{y}' + \text{y}^2 + 1 = 0$

The volume of a spherical balloon is increasing at the rate of $25 \ cm^3 / \sec$. Find the rate of change of its surface area at the instant when radius is $5 \ cm.$

Let R be the equivalence relation on the set Z of the integers given by R = {(a, b): 2 divides a - b}. Write the equivalence class [0].

Write the equation of the plane parallel to XOY- plane and passing through the point (2, -3, 5).

Give an example of a relation which is,
Symmetric and transitive but not reflexive.

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

For each of the exercises given below, verify that the given function (implicit or explicit) is a solution of the corresponding differential equation.

$\text{y}=\text{a e}^{\text{x}}+\text{b e}^{-\text{x}}+\text{x}^2$

$\text{x}\frac{\text{d}^2\text{y}}{\text{dx}^2}+2\frac{\text{dy}}{\text{dx}}-\text{xy}+\text{x}^2-2=0$

Evaluate the following:
$\sec^{-1}\Big(\sec\frac{25\pi}{6}\Big)$

Evaluate the following:
$\sec^{-1}\Big(\sec\frac{5\pi}{4}\Big)$