x-1 x+4 dx - Vidyadip

Question

$\int\frac{\text{x}-1}{\sqrt{\text{x}+4}}\ \text{dx}$

✓

Answer

$\text{Let I} =\int\Big(\frac{\text{x}-1}{\sqrt{\text{x}+4}}\Big)\text{dx}$
Putting x + 4 = t
Then, x = t - 4
Difference both sides
dx = dt
Now integral becomes,
$\text{I}=\int\Big(\frac{\text{t}-4-1}{\sqrt{\text{t}}}\Big)\text{dt}$
$=\int\Big(\frac{\text{t}}{\sqrt{\text{t}}}-\frac{5}{\sqrt{\text{t}}}\Big)\text{dt}$
$=\int\Big(\text{t}^{\frac{1}{2}}-5\text{t}^{-\frac{1}{2}}\Big)\text{dt}$
$=\frac{\text{t}^{\frac{1}{2}+1}}{\frac{1}{2}+1}-5\frac{\text{t}^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}+\text{C}$
$=\frac{2}{3}\text{t}^\frac{3}{2}-10\sqrt{\text{t}}+\text{C}$
$=\frac{2}{3}(\text{x}+4)^\frac{3}{2}-10(\text{x}+4)^\frac{1}{2}+\text{C}$

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 "5 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

Using differentials, find the approximate values of the following:
$\sin\Big(\frac{22}{14}\Big)$

Show that the semi-vertical angle of the cone of the maximum value and of given slant height is ${\tan ^{ - 1}}\sqrt 2$

If $\text{A}=\begin{bmatrix}1&2\\2&1\end{bmatrix}, f(x) = x^2 - 2x - 3$, show that $f(A) = 0$

Show that the relative error in computing the volume of a sphere, due to an error in measuring the radius, is approximately equal to three times the relative error in the radius.

At what points on the curve $y = x^2 - 4x + 5$ is the tangent perpendicular to the line $2y + x = 7?$

Maximise Z = x + y, subject to $\text{x}-\text{y}\leq-1,\ -\text{x}+\text{y}\leq0,\ \text{x},\ \text{y}\geq0.$

It is given that the Rolle's theorem holds for the function $f(x) = x^3 + bx^2 + cx, \text{x}\in[1,2]$ at the point $\text{x}=\frac{4}{3},$ the values of b and c.

Let $\text{F}(\alpha)=\begin{bmatrix}\cos\alpha & -\sin\alpha & 0 \\ \sin\alpha & \cos\alpha & 0 \\ 0 & 0 & 1\end{bmatrix}$$\text{and G }(\beta)=\begin{bmatrix} \cos\beta & 0 & \sin\beta \\ 0 & 1 & 0 \\ -\sin\beta & 0 & \cos\beta \end{bmatrix}$
Show that$\big[\text{F}(\alpha)\text{G}(\beta)\big]^{-1}=\text{G}(-\beta)\text{F}(-\alpha).$

Show that the family of curves for which $\frac{\text{dy}}{\text{dx}}=\frac{\text{x}^2+\text{y}^2}{2\text{xy}},$ is given by $\text{x}^2-\text{y}^2=\text{Cx}$

Find the angles which the vector $\vec{\text{a}}=\hat{\text{i}}-\hat{\text{j}}+\sqrt{2}\hat{\text{k}}$ makes with the coordinate axes.