Mathematics

$$\displaystyle\int \limits_{ -1 }^{ 1 }|x| dx = a$$ then -


ANSWER

$$a=1$$


SOLUTION
Given,
$$\displaystyle\int \limits_{ -1 }^{ 1 }|x| dx$$
$$=2\displaystyle\int \limits_{ 0 }^{ 1 }x dx$$ [ Since $$|x|$$ is an even function]
$$=2\times \left[\dfrac{x^2}{2}\right]_{0}^{1}$$
$$=2\times \dfrac{1}{2}$$
$$=1$$.
View Full Answer

Its FREE, you're just one step away


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

Realted Questions

Q1 Single Correct Medium
$$\int_{0}^{a} \dfrac{d x}{x+\sqrt{a^{2}-x^{2}}}$$ is
  • A. $$\dfrac{a^{2}}{4}$$
  • B. $$\dfrac{\pi}{2}$$
  • C. $$\pi$$
  • D. $$\dfrac{\pi}{4}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Medium
$$ \int \dfrac {x+2}{(x^2 + 3x +3) \sqrt{x+1} } dx $$ is equal to :
  • A. $$ \dfrac {1}{ \sqrt3} \tan^{-1} \left( \dfrac {x} { \sqrt{3(x+1)} } \right) + C $$
  • B. $$ \dfrac {1}{ \sqrt3} \tan^{-1} \left( \dfrac {x} { \sqrt{x+1} } \right) + C $$
  • C. None of these
  • D. $$ \dfrac {2}{ \sqrt3} \tan^{-1} \left( \dfrac {x} { \sqrt{3(x+1)} } \right) + C $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Medium
If $$\int { \cfrac { \left( { x }^{ 2 }+1 \right) \left( { x }^{ 2 }+4 \right)  }{ \left( { x }^{ 2 }+3 \right) \left( { x }^{ 2 }-5 \right)  }  } dx=\int { \left\{ 1+\cfrac { f(x) }{ \left( { x }^{ 2 }+3 \right) \left( { x }^{ 2 }-5 \right)  }  \right\}  } dx$$
$$x+A\tan ^{ -1 }{ \left( \cfrac { x }{ A' }  \right)  } +B\log { \left( \cfrac { x-l }{ x+m }  \right)  } +K\quad $$ then which of the following is correct
  • A. $$A=\cfrac { 1 }{ 4\sqrt { 3 } } ,B=\cfrac { 27 }{ 8\sqrt { 5 } } ,K\in R$$
  • B. $$f(x)=7{ x }^{ 2 }+19,A'=\sqrt { 3 } ,K\in R$$
  • C. $$l=m=\sqrt { 5 } ,L=1,K\in R$$
  • D. All of these

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
Evaluate:  $$\displaystyle\int \dfrac{(1+x+x^2)dx}{x(1+x^2)}$$.
  • A. $$2lnx + tan^{-1}x + C$$
  • B. $$lnx + 2tan^{-1}x + C$$
  • C. $$lnx +4 tan^{-1}x + C$$
  • D. $$lnx + tan^{-1}x + C$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Passage Hard
Let us consider the integral of the following forms
$$f{(x_1,\sqrt{mx^2+nx+p})}^{\tfrac{1}{2}}$$
Case I If $$m>0$$, then put $$\sqrt{mx^2+nx+C}=u\pm x\sqrt{m}$$
Case II If $$p>0$$, then put $$\sqrt{mx^2+nx+C}=u\pm \sqrt{p}$$
Case III If quadratic equation $$mx^2+nx+p=0$$ has real roots $$\alpha$$ and $$\beta$$, then put $$\sqrt{mx^2+nx+p}=(x-\alpha)u\:or\:(x-\beta)u$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer