Question

Find the Integral of the given function w.r.t x

$Y=3x^2-\frac{1}{\sqrt{x}}$

• A. $3x^3-2\sqrt{x}$ + c
• B. $x^3-2\sqrt{x}$
• C. $6x+\frac{1}{2(x{)}^{3/2}}$
• D. $x^3-2\sqrt{x}+c$

Answer 1

The correct option is D

$x^3-2\sqrt{x}+c$

$Y=3x^2-\frac{1}{\sqrt{x}}$

$\int (3x^2-\frac{1}{\sqrt{x}})dx$ = $\int 3x^{2}dx-\int \frac{1}{\sqrt{x}}dx$

$3\times \frac{x^3}{3}+c_1-\int x^{\frac{-1}{2}}dx$ $(\because \int x^{n}dx=\frac{x^{n+1}}{n+1}+c)$

$x^3+c_1-2\sqrt{x}+c_2$

$\Rightarrow x^3-2\sqrt{x}+c(\because c_1+c_2=c)$