Question

Write an anti derivative for each of the following functions using the method of inspection:
i) $\cos 2x$
ii) $3x^2+4x^3$
iii) $\frac{1}{x},x\ne 0$

Answer 1

(i) Let $F\left(x\right)=2sin2x$

that

$f^{\prime }\left(x\right)2\times \frac{\cos 2x}{2}$

$=\cos 2x$

therefore quantitative of $cos2xis2sin2x$

(ii) Let $F\left(x\right)=x^3+x^4$

then $F^{\prime }\left(x\right)=3x^2+4x^3$

thus quantitative of $3x^2+4x^3$

is $x^3+x^4$

(iii) Let $f\left(x\right)=logx$

$F\left(x\right)=\frac{1}{x}$

therefore quantitative of $\frac{1}{x}$ is $logx$