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

Question

Write a value of $\int\text{e}^{\text{x}}(\sin\text{x}+\cos\text{x})\text{dx}$

✓

Answer

Let $\text{I}=\int\text{e}^{\text{x}}(\sin\text{x}+\cos\text{x})\text{dx}$
$\because\ \int\text{e}^{\text{x}}\big(\text{f(x})+\text{f}'(\text{x})\big)\text{dx}=\text{e}^{\text{x}}\text{f(x)}+\text{C}$
Here, $\text{f(x)}=\sin\text{x}$ and $\text{f}'(\text{x})=\cos\text{x}$
$\therefore\ \text{I}=\int\text{e}^{\text{x}}(\sin\text{x}+\cos\text{x})\text{dx}=\text{e}^{\text{x}}\sin\text{x}+\text{C}$

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 "Solve the Following Question.(3 Marks)" from Indefinite Integrals→Indefinite Integrals — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Evaluate the following:

$\int_1^{\infty} \frac{1}{\sqrt{x}(1+x)} d x$

Represent the following families of curves by forming the corresponding differential equation:
$(\text{x}-\text{a})^2-\text{y}^2=1$

For the principal values, evaluate the following:
$\tan^{-1}\big(\sqrt3\big)-\sec^{-1}(-2)$

Find $|\vec{\text{a}|}$ and $\big|\vec{\text{b}}\big|$ if
$\big(\vec{\text{a}}+\vec{\text{b}}\big).\big(\vec{\text{a}}-\vec{\text{b}}\big)=12$ and $|\vec{\text{a}}|=2\big|\vec{\text{b}}\big|$

Solve the following differential equations:$\frac{\text{dy}}{\text{dx}}=\text{y}\sin2\text{x, y}(0)=1$

Ten eggs are drawn successively, with replacement, from a lot containing 10% defective eggs. Find the probability that there is at least one defective egg.

Evaluate the following integrals:
$\int\text{x}^2\text{e}^{\text{x}^3}\cos\big(\text{e}^{\text{x}^3}\big)\text{dx}$

If $\text{y}=\sin(\log\text{x})$ prove that $\text{x}^2\frac{\text{d}^2\text{y}}{\text{dx}^2}+\text{x}\frac{\text{dy}}{\text{dx}}+\text{y}=0$

Find the vector equation of a plane at a distance 6 units from the origin and to which vector $2 \hat{ i }-\hat{ j }+2 \widehat{ k }$ is normal

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