Evaluate the following integrals: 1 x^ 3 2 dx - Vidyadip

Question

Evaluate the following integrals:
$\int\frac{1}{\text{x}^{\frac{3}{2}}}\text{dx}$

✓

Answer

$\int\frac{1}{\text{x}^\frac{3}{2}}\text{dx}=\int\text{x}\frac{-3}{2}\text{dx}$
$=\int\text{x}^\frac{-3}{2}\text{dx}$
$=\frac{\text{x}^{\frac{-3}{2}+1}}{\frac{-3}{2}+1}+\text{c}$
$=\frac{\text{x}^\frac{-1}{2}}{\frac{-1}{2}}+\text{c}$
$=-2\text{x}\frac{1}{\sqrt{\text{x}}}+\text{c}$
$=\frac{-2}{\sqrt{\text{x}}}+\text{c}$

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 : $\int_0^\pi x \cdot \sin ^2 x \cdot d x$

Evaluate the following:

$\int x^2 \sin 3 x d x$

Eight coins are thrown simultaneously. Find the chance of obtaining at least six heads.

Find the differential equation of all circles having radius 9 and centre at point (h, k).

Using truth tables, examine whether the statement pattern $(p \wedge q) \vee(p \wedge r)$ is a tautology, contradiction or contingency.

Find the co-ordinates of the points of intersection of the lines represented by $x^2-y^2-2 x+1$ = 0.

Find the area of the region bounded by the curves $x^2 = 8y, y = 2, y = 4$ and the $Y-$axis, lying in the first quadrant

For the binary operation multiplication modulo $10 (\times _{10})$ defined on the set $S = \{1, 3, 7, 9\},$ write the inverse of $3.$

Evaluate the following:

$\int x \sin ^{-1} x d x$

$\int_{-\pi / 4}^{\pi / 4} \frac{1}{1-\sin x} \cdot d x$