Evaluate the following integrals: x^2-2x dx

Question

Evaluate the following integrals:
$\int\sqrt{\text{x}^2-2\text{x}}\text{dx}$

✓

Answer

Let $\text{I}=\int\sqrt{\text{x}^2-2\text{x}}\text{dx}$
$\Rightarrow\text{I}=\int\sqrt{\text{x}^2-2\text{x}+1-1}\text{dx}$
$\Rightarrow\text{I}=\int\sqrt{(\text{x}-1)^2-1^2}\text{dx}$
$\because\ \int\sqrt{\text{x}^2-\text{a}^2}\text{dx}=\frac{\text{x}}{2}\sqrt{\text{x}^2-\text{a}^2}-\frac{\text{a}^2}{2}\ln\big(|\text{x}+\sqrt{\text{x}^2-\text{a}^2}|\big)+\text{C}$
$\therefore\ \text{I}=\frac{(\text{x}-1)}{2}\sqrt{(\text{x}-1)^2-1}-\frac{1}{2}\ln\big|(\text{x}-1)+\sqrt{\text{x}^2-2\text{x}}\big|+\text{C}$

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 integrals:$\int\frac{1}{\sqrt{8+3\text{x}-\text{x}^2}}\text{ dx}$

→

Find the area of the parallelogram determinrd by the vectors:
$2\hat{\text{i}}+\hat{\text{j}}+3\hat{\text{k}}$ and $\hat{\text{i}}-\hat{\text{j}}$

→

If $\mathrm{u}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{k}, \bar{v}=3 \hat{\mathbf{i}}+\hat{k}$ and $\bar{w}=\hat{\mathbf{j}}-\hat{\mathbf{k}}$ are given vectors, then find

(i) $[\bar{u}+\bar{w}] \cdot[(\bar{w} \times \bar{r}) \times(\bar{r} \times \bar{w})]$

Question is modified.

If $\bar{u}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{k}, \bar{r}=3 \hat{\mathbf{i}}+\hat{k}$ and $\bar{w}=\hat{\mathbf{j}}-\hat{\mathbf{k}}$ are given vectors, then find $[\bar{u}+\bar{w}] \cdot[(\bar{u} \times$

$\bar{r}) \times(\bar{r} \times \bar{w})]$

→

Show that $\text{AB}\neq\text{BA}$ in the following cases:
$\text{A}=\begin{bmatrix}1&3&0\\1&1&0\\4&1&0\end{bmatrix}$ and $\text{B}=\begin{bmatrix}0&1&0\\1&0&0\\0&5&1\end{bmatrix}$

→

Find fog and gof if:$f(x) = x^2 + 2$, $\text{g(x)}=1-\frac{1}{1-\text{x}}$

→

Differentiate the following functions with respect to x:
$2^{\text{x}^3}$

→

Find fog and gof if:f(x) = |x|, g(x) = sinx

→

Find the coordinates of the foot of perpendicular from the origin to the plane $2x + 6y − 3z = 63$

→