Evaluate the following functions : (3 x+2) x-4 d x - Vidyadip

Question

Evaluate the following functions : $\int(3 x+2) \sqrt{x-4} \cdot d x$

✓

Answer

$
\begin{aligned}
& \text { put } \quad x-4=t \\
& \therefore \quad x=4+t
\end{aligned}
$
Differentiate
$
\begin{aligned}
& 1 \cdot d x=1 \cdot d t \\
= & \int[3(4+t)+2] \cdot \sqrt{t} \cdot d t \\
= & \int(14+3 t) \cdot t^{\frac{1}{2}} \cdot d t \\
= & \int\left(14 t^{\frac{1}{2}}+3 t^{\frac{3}{2}}\right) \cdot d t \\
= & 14 \frac{t^{\frac{3}{2}}}{\frac{3}{2}}+3 \frac{t^{\frac{5}{2}}}{\frac{5}{2}} \cdot d x \\
= & \frac{28}{3}(x-4)^{\frac{3}{2}}+\frac{6}{5}(x-4)^{\frac{5}{2}}+c
\end{aligned}
$

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.(2 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

Find the general solution of :$\cos \theta=-\frac{1}{2}$

Reduce each of the following differential equations to the variable separable form and hence solve:

$\cos ^2(x-2 y)=1-2 \frac{d y}{d x}$

Find $\vec{\text{a}}.\vec{\text{b}}$ when
$\vec{\text{a}}=\hat{\text{j}}+2\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{i}}+\hat{\text{k}}$

f A is a matrix of order $3\times 4$ and B is a matrix of order $4\times 3$, find the order of the matrix of AB.

Evaluate : $\int_0^{\frac{\pi}{4}} \sec ^4 x d x$

An urn contains 7 red and 4 blue balls. Two balls are drawn at random with replacement. Find the probability of getting,
2 red balls.

$\text{Show that lines :}\bar{r}=(\hat{i}+\hat{j}-\hat{k})+\lambda(2 \hat{i}-2 \hat{j}+\hat{k}) \text { and } \bar{r}=(4 \hat{i}-3 \hat{j}+2 \hat{k})+\mu(\hat{i}-2 \hat{j}+2 \hat{k})$ intersect each other.

If A and B are square matrices of the same order, explain, why in general:
$(A − B)^2 \neq A^2 − 2AB + B^2$

If $\vec{\text{a}}$ and $\vec{\text{b}}$ are mutually perpendicular unit vectors, write the value of $\big|\vec{\text{a}}+\vec{\text{b}}\big|.$

Determine the order and degree of each of the following differential equations:

$\frac{d^2 y}{d t^2}+\left(\frac{d y}{d t}\right)^2+7 x+5=0$