Write an anti derivative of function using the method of inspecti… - Vidyadip

Question

Write an anti derivative of function using the method of inspection: $\frac{1}{x}, x \neq 0$

✓

Answer

We know that
$\frac{d}{d x}(\log x)=\frac{1}{x}, x>0$ and $\frac{d}{d x}[\log (-x)]=\frac{1}{-x}(-1)=\frac{1}{x}, x<0$
Combining above, we get $\frac{d}{d x}(\log |x|)=\frac{1}{x}, x \neq 0$
Therefore, $\int \frac{1}{x} d x=\log |x|$ is one of the anti derivatives of $\frac{1}{x}$

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 "1 Marks Question" from Integrals→Integrals — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Find the vector equation of the plane with intercepts $\text{3, -4 and 2 on } x, y \text{ and } z-\text{axis}$ respectively.

Given that E and F are events such that $\text{P}(\text{E})=0.6,\ \text{P}(\text{F})=0.3\ \text{and}\ \text{P}(\text{E}\cap\text{F})=0.02,\ \text{find}\ \text{P}(\text{E}|\text{F})\ \text{and}\ \text{P}(\text{F}|\text{E}) .$

Write the degree of the following differrntial equation $ \Big(\frac{\text{dy}}{\text{dx}}\Big)^{4}+3\text{x}\frac{\text{d}^{2}\text{y}}{\text{dx}^{2}}=0.$

Show that function $F ( x )=\frac{1}{(x-a)}$, is discontinuous at $x=a$.

$\int \frac{d x}{x\left(x^{2}+1\right)}$ equals

Write a vector of magnitude 15 units in the direction of vector.

Integrate the functions in Exercises:
$\frac{\cos\sqrt{\text{x}}}{\sqrt{\text{x}}}$

Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b > 6}.

Prove that $\cos ^ { - 1 } \left( \frac { 12 } { 13 } \right) + \sin ^ { - 1 } \left( \frac { 3 } { 5 } \right) = \sin ^ { - 1 } \left( \frac { 56 } { 65 } \right).$

Find the vector equation of a plane which is at a distance of 5 units from the origin and its normal vector is $2\hat{\text{i}} - 3\hat{\text{j}} + 6\hat{\text{k}}.$