Mathematics

$$\displaystyle\int\limits_{a}^{b}f(x)\ dx=b^3-a^3$$, then find $$f(x)$$.


SOLUTION
Given,
$$\displaystyle\int\limits_{a}^{b}f(x)\ dx=b^3-a^3$$.
Let, $$f(x)=3x^2$$
Then,
$$\displaystyle\int\limits_{a}^{b}f(x)\ dx$$
$$=\displaystyle\int\limits_{a}^{b}3x^2\ dx$$
$$=3\left[\dfrac{x^3}3{}\right]_{x=a}^{x=b}$$
$$=(b^3-a^3)$$
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 111
Enroll Now For FREE

Realted Questions

Q1 Subjective Hard
Evaluate $$\displaystyle \int_{0}^{\pi}\mathrm{e}^{|\mathrm{c}\mathrm{o}\mathrm{s}\mathrm{x}|}(2\sin(\frac{1}{2}\cos \mathrm{x})+3\cos(\frac{1}{2}\cos \mathrm{x})) \sin x dx $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Medium
The value of $$\displaystyle \int_{3}^{5}\frac{x^{2}}{x^{2}-4} dx$$ is
  • A. $$2(1-\displaystyle \mathrm{l} \mathrm{o}\mathrm{g}_{\mathrm{e}}(\frac{15}{7}))$$
  • B. $$2(1+4\log_{\mathrm{e}}3-4\log_{\mathrm{e}}7+4\log_{\mathrm{e}}5)$$
  • C. $$2(1-\displaystyle \tan^{-1}(\frac{15}{7}))$$
  • D. $$2(1+\displaystyle \mathrm{l}\mathrm{o}\mathrm{g}_{\mathrm{e}}(\frac{15}{7}))$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Medium
$$\displaystyle \int { \frac { \sec { x }  }{ \sqrt { \sin { \left(2 x+\alpha  \right)  } +\sin { \alpha  }  }  } dx } =$$
  • A. $$\displaystyle \sqrt { 2\left( \sin { x } +\tan { \alpha  }  \right) \sec { \alpha  }  } $$
  • B. $$\displaystyle \sqrt { \left( \tan { x } +\tan { \alpha  }  \right) \sec { \alpha  }  } $$
  • C. None of these
  • D. $$\displaystyle \sqrt { 2\left( \tan { x } +\tan { \alpha  }  \right) \sec { \alpha  }  } $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium

$$\displaystyle \int_{1}^{2}\frac{dx}{x^{2}-2x+4}=$$
  • A.
  • B. $$\displaystyle \frac{\pi}{2}$$
  • C. $$\displaystyle \frac{\pi}{3}$$
  • D. $$\displaystyle \frac{\pi}{6\sqrt{3}}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Passage Medium
Let $$n \space\epsilon \space N$$ & the A.M., G.M., H.M. & the root mean square of $$n$$ numbers $$2n+1, 2n+2, ...,$$ up to $$n^{th}$$ number are $$A_{n}$$, $$G_{n}$$, $$H_{n}$$ and $$R_{n}$$ respectively. 
On the basis of above information answer the following questions

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer