Mathematics

$$\int _ { 0 } ^ { 4 } \frac { \sin x ^ { 2 } d x } { \sin ( x - 4 ) ^ { 2 } + \sin x ^ { 2 } }$$ is equal to


ANSWER

2


SOLUTION
$$I=\int _{ 0 }^{ 4 }{ \frac { \sin { { x }^{ 2 } }  }{ \sin { { \left( x-4 \right)  }^{ 2 } } +\sin { { x }^{ 2 } }  } dx } \\ I=\int _{ 0 }^{ 4 }{ \frac { \sin { { \left( 4-x \right)  }^{ 2 } }  }{ \sin { { x }^{ 2 } } +\sin { { \left( 4-x \right)  }^{ 2 } }  } dx } \quad \quad \quad \left( \int _{ a }^{ b }{ f\left( x \right) dx } =\int _{ a }^{ b }{ f\left( a+b-x \right) dx }  \right) \\ 2I=\int _{ 0 }^{ 4 }{ \left( \frac { \sin { { x }^{ 2 } }  }{ \sin { { \left( x-4 \right)  }^{ 2 } } +\sin { { x }^{ 2 } }  } +\frac { \sin { { \left( 4-x \right)  }^{ 2 } }  }{ \sin { { x }^{ 2 } } +\sin { { \left( 4-x \right)  }^{ 2 } }  }  \right)  } dx\\ \quad =\int _{ 0 }^{ 4 }{ dx } =4\\ \Rightarrow I=2$$
so option A is correct
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 84
Enroll Now For FREE

Realted Questions

Q1 Single Correct Hard
If $$\displaystyle \int _{ 0 }^{ \infty  }{ { e }^{ -ax }dx } =\frac { 1 }{ a } $$, then $$\displaystyle \int _{ 0 }^{ \infty  }{ { x }^{ n }{ e }^{ -ax }dx } $$ is
  • A. $$\displaystyle \frac { { \left( -1 \right)  }^{ n }n! }{ { a }^{ n+1 } } $$
  • B. $$\displaystyle \frac { { \left( -1 \right)  }^{ n }\left( n-1 \right) ! }{ { a }^{ n } } $$
  • C. None of these
  • D. $$\displaystyle \frac { n! }{ { a }^{ n+1 } } $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Hard
Evaluate:
$$\int { \cfrac { 8 }{ (x+2)({ x }^{ 2 }+4) } dx } $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Subjective Hard
Integrate
$$\int {{x \over {{x^2} + x + 1}}dx} $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Multiple Correct Hard
$$\int_{0}^{2\pi}sin^{4}$$ x dx is equal to
  • A. $$8\int_{0}^{\frac{\pi}{4}}sin^{4}$$ x dx
  • B. $$3\int_{0}^{\frac{2\pi}{3}}sin^{4}$$ x dx
  • C. $$2\int_{0}^{\pi}sin^{4}$$ x dc
  • D. $$4\int_{0}^{\frac{\pi}{2}}cos^{4}$$ x dx

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Easy
Evaluate:
$$ \int_{}^{} {\frac{{ - 1}}{{\sqrt {1 - {x^2}} }}dx} $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer