Mathematics

Solve :
$$\displaystyle \int_1^2(4x^3-5x^2+6x+9)dx$$


SOLUTION
$$\int _{ 1 }^{ 2 }{ (4{ x }^{ 3 } } -5{ x }^{ 2 }+6x+9)dx\\ =\int _{ 1 }^{ 2 }{ { x }^{ 4 } } -\frac { 5{ x }^{ 3 } }{ 3 } +3{ x }^{ 2 }+9x\\ =(15-\frac { 40 }{ 3 } +12+18)-(1-\frac { 5 }{ 3 } +3+9)\\ =\frac { 61 }{ 3 } $$
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 Medium
Find the antiderivative $$F$$ of $$f$$ defined by $$f(x)=4x^3 -6$$, where $$f(0)=3$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Medium
$$\displaystyle \int_{-\pi }^{\pi}\left ( \cos ax-\sin bx \right )^{2}dx$$ where a and b are integer is equal to
  • A. $$\displaystyle -\pi $$
  • B. $$0$$
  • C. $$\displaystyle \pi $$
  • D. $$\displaystyle 2\pi $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Hard
Primitive of $$\displaystyle \sqrt[3]{\frac{x}{(x^{4} - 1)^{4}}}$$  w.r.t  is
  • A. $$ \displaystyle \frac{-3}{4}(1 + x^{-4})^{\tfrac{1}{3}} + C$$
  • B. $$ \displaystyle \frac{-3}{4}(1 + x^{-4})^{\tfrac{-1}{3}} + C$$
  • C. $$ \displaystyle \frac{3}{4}(1 - x^{-4})^{\tfrac{1}{3}} + C$$
  • D. $$ \displaystyle \frac{-3}{4}(1 - x^{-4})^{\tfrac{-1}{3}} + C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
Solve: $$\int_{0}^{\pi/4}\log (1 + \tan x) dx$$.
  • A. $$\dfrac{\pi}{7}\log2$$
  • B. $$-\dfrac{\pi}{8}\log2$$
  • C. None of these
  • D. $$\dfrac{\pi}{8}\log2$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Single Correct Medium

Find $$\displaystyle \int_{0}^{\frac{\pi}{2}}\frac{\sec^{2}xdx}{(\sec x+\tan x)^{n}}$$, where $$(\mathrm{n}>2)$$
  • A. $$\displaystyle \frac{1}{n^{2}-1}$$
  • B. $$\displaystyle \frac{n}{n^{2}+1}$$
  • C. $$\displaystyle \frac{2}{n^{2}-1}$$
  • D. $$\displaystyle \frac{n}{n^{2}-1}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer