Mathematics

Solve :- $$\displaystyle \int_0^1 \ 3^x dx$$


SOLUTION
$$3 = \ e^{ \ln3}$$
$$\implies 3^x = e^{\ x\ln3}$$

$$\therefore \displaystyle\int_0^13^xdx = \displaystyle\int_0^1e^{x\ln3}dx $$

$$=\dfrac{1}{\ln3}[e^{x\ln3}]_0^1=\dfrac{1}{\ln3}[e^{\ln3}-1]$$

$$=\dfrac{3-1}{\ln3}$$

$$=\boxed{\dfrac{2}{\ln3}}$$
View Full Answer

Its FREE, you're just one step away


Subjective Medium Published on 17th 09, 2020
Next Question
Questions 203525
Subjects 9
Chapters 126
Enrolled Students 86
Enroll Now For FREE

Realted Questions

Q1 Subjective Medium
$$\displaystyle\int 5^{x + \tan^{-1}x}\left(\dfrac{x^2 + 2}{x^2 + 1}\right)dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Medium
If $$l_{n}=\displaystyle \int{\dfrac{t^{n}}{1+t^{2}}}dt$$ then
  • A. $$l_{n+1}=\dfrac{t^{n+1}}{n+1}l_{n}$$
  • B. $$l_{n+1}=\dfrac{t^{n-1}}{n-1}l_{n}$$
  • C. $$l_{n21}=\dfrac{t^{n+1}}{n+1}l_{n}$$
  • D. $$l_{n+2}=\dfrac{t^{n}}{n}-nl_{n}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Medium
Evaluate the integral
$$\displaystyle \int_{\pi/4}^{\pi /2}l {o} {g}(1+ {c} {o} {t} {x}) {d} {x}$$
  • A. $$\displaystyle \frac{\pi}{4}\log2$$
  • B. $$\pi\log 2$$
  • C. $$0$$
  • D. $$\displaystyle \frac{\pi}{8}$$ $$\log 2$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
The value of $$\displaystyle \int _{ 0 }^{ \pi  }{ \sin ^{ 50 }{ x } \cos ^{ 49 }{ x } dx } $$ is
  • A. $$\dfrac{\pi}{4}$$
  • B. $$\dfrac{\pi}{2}$$
  • C. $$1$$
  • D. $$0$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Medium
$$\int { \cfrac { f'(x) }{ f(x) } dx } =\log { [f(x)] } +c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer