Find an anti-derivative for the following fun | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) To find the anti-derivative of $f(x) = 3x^{2} + 4x^{3}$ by the method of inspection,we look for a function $F(x)$ such that $F'(x) = f(x)$.We know

Vedclass · Accepted Answer

$x^{3} + x^{4}$

Vedclass · Answer

(A) To find the anti-derivative of $f(x) = 3x^{2} + 4x^{3}$ by the method of inspection,we look for a function $F(x)$ such that $F'(x) = f(x)$.We know that the derivative of $x^{n}$ is $nx^{n-1}$.For the first term $3x^{2}$,we observe that $\frac{d}{dx}(x^{3}) = 3x^{2}$.For the second term $4x^{3}$,we observe that $\frac{d}{dx}(x^{4}) = 4x^{3}$.By the linearity property of derivatives,we have:$\frac{d}{dx}(x^{3} + x^{4}) = \frac{d}{dx}(x^{3}) + \frac{d}{dx}(x^{4}) = 3x^{2} + 4x^{3}$.Therefore,an anti-derivative of $3x^{2} + 4x^{3}$ is $x^{3} + x^{4}$.

Find an anti-derivative for the following function using the method of inspection:
$3x^{2} + 4x^{3}$

Similar Questions

$\int \frac{\sin \frac{5x}{2}}{\sin \frac{x}{2}} dx = $ (where $C$ is a constant of integration.)

If $f\left(\frac{2 x+3}{3 x+5}\right)=x+4$,where $x \neq \frac{-5}{3}, \frac{-2}{3}$,and $\int f(x) d x=A x+B \ln |3 x-2|+C$,then $3 B-A=$

If $\int \frac{dx}{x^2+2x+2}=f(x)+c$,then $f(x)$ is equal to :

$\int {\frac{{\cot x \tan x}}{{{{\sec }^2}x - 1}}} \;dx = $

$\int \frac{\sin^3 x + \cos^3 x}{\sin^2 x \cos^2 x} \, dx = $

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Find an anti-derivative for the following function using the method of inspection:$3x^{2} + 4x^{3}$