Mathematics

Evaluate the given integral: $$\displaystyle \int_{0}^{4} {(4x-x^2)}dx$$


SOLUTION

Consider, $$I=\displaystyle \int_{0}^{4} {(4x-x^2)}dx$$

$$I=\left[ 2x^2-\dfrac{x^3}3 \right]_0^4$$

$$I=32-\dfrac{64}3$$

$$I =\dfrac {32}3$$

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 84
Enroll Now For FREE

Realted Questions

Q1 Single Correct Medium
$$\displaystyle \int \dfrac{x-\sin{x}}{1-\cos{c}}dx$$
  • A. $$-x\cot{\dfrac{x}{2}}+c$$
  • B. $$\cot{\dfrac{x}{2}}+c$$
  • C. $$None \ of\ these$$
  • D. $$x\cot{\dfrac{x}{2}}+c$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Hard
$$\displaystyle \int x.\sqrt{\left [ \frac{2\sin \left ( x^{2}-1 \right )-\sin 2\left ( x^{2}-1 \right )}{2\sin \left ( x^{2}-1 \right )+\sin 2\left ( x^{2}-1 \right )} \right ]}dx$$ where $$\displaystyle x^{2}-1\neq n\pi $$
  • A. $$\displaystyle \log \sec {x^{2}-1}.$$
  • B. $$\displaystyle \log \tan \frac{x^{2}-1}{2}.$$
  • C. $$\displaystyle \log \cos \frac{x^{2}-1}{2}.$$
  • D. $$\displaystyle \log \sec \frac{x^{2}-1}{2}.$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Medium
$$\displaystyle\int\limits_{a}^{b}f(x)\ dx=b^3-a^3$$, then find $$f(x)$$.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Hard
lf $$f(x)=\displaystyle \frac{x+2}{2x+3}$$ , then $$\displaystyle \int(\frac{f(x)}{x^{2}})^{1/2}dx$$ is

equal to
$$\displaystyle \frac{1}{\sqrt{2}}g(\frac{1+\sqrt{2f(x)}}{1-\sqrt{2f(x)}})-\sqrt{\frac{2}{3}}h(\frac{\sqrt{3f(x)}+\sqrt{2}}{\sqrt{3f(x)}-\sqrt{2}})+c$$ 
where
  • A. $$g(x)=\tan^{-1}x,\ h(x)=\log|x|$$
  • B. $$g(x)=\log|x|,h(x)=\tan^{-1}x$$
  • C. $$g(x)=h(x)=\tan^{-1}x$$
  • D. $$g(x)=\log|x|, h(x)=\log|x|$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Single Correct Medium
If $$I=\displaystyle \int^{e}_{\dfrac {1}{e}}|\log|.\dfrac {dx}{x^{2}}$$ then  $$I=$$
  • A. $$\dfrac {2}{e}$$
  • B. $$2\left(1-\dfrac {1}{e}\right)$$
  • C. $$0$$
  • D. $$2$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer