Evaluate: 1 a^xb^x dx - Vidyadip

Question

Evaluate:
$\int\frac{1}{\text{a}^\text{x}\text{b}^\text{x}}\text{dx}$

✓

Answer

$\int\frac{1}{\text{a}^\text{x}\text{b}^\text{x}}\text{dx}=\int\text{a}^{-\text{x}}\text{b}^{-\text{x}}\text{dx}$
$=\int(\text{ab})^{-\text{x}}\text{dx}$
$=\frac{(\text{ab})^{-\text{x}}}{\log_\text{e}(\text{ab})^{-1}}+\text{c}$
$=\frac{(\text{ab})^{-\text{x}}}{-\log_\text{e}(\text{ab})}+\text{c}$
$=\frac{\text{a}^{-\text{x}}\text{b}^{-\text{x}}}{-\log_\text{e}(\text{ab})}+\text{c}$

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.(2 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

Find the general solution of : $\sin \theta=-\frac{\sqrt{3}}{2}$

Find points on the curve given by $y=x^3-6 x^2+x+3$ where the tangents are parallel to the line
$y=x+5 .$

Find the approximate values of:

$\log _{10}(1016)$, given that $\log _{10} e=0.4343$

Define a commutative binary operation on a set.

Using truth tables prove the following logical equivalences : (p ∧ q) → r ≡ p → (q → r)

Evaluate : $\int \frac{1}{4 x^2+11} \cdot d x$

$\int \sqrt{1+\sin 5 x} \cdot d x$

Find the equation of the curve which passes through the point (3, -4) and has slope $\frac{2\text{y}}{\text{x}}$ at any point (x, y) on it.

Find the projection of $\vec{\text{a}}$ on $\vec{\text{b}}$ if $\vec{\text{a}}.\vec{\text{b}}=8$ and $\vec{\text{b}}=2\hat{\text{i}}+6\hat{\text{j}}+3\hat{\text{k}}.$

Five cards are drawn successively with replacement from a well-shuffled pack of 52 cards. What is the probability that
all the five cards are spades?