Mathematics

Evaluate the following integrals:
$$\int { \cfrac { \sin { 8x }  }{ \sqrt { 9+\sin ^{ 4 }{ 4x }  }  }  } dx$$


SOLUTION
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 Subjective Medium
Evaluate the following integral
$$\int { \cfrac {2\cos { 4x } -\cos { 2x }  }{ \sin { 4x } -\sin { 2x }  }  } dx\quad $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Single Correct Medium
Evaluate: $$\int _{ a }^{ b }{ x } dx$$ using limit of sum.
  • A. $$\dfrac{b^2-a^2}{3}$$
  • B. $$\dfrac{b^2+a^2}{2}$$
  • C. None of these
  • D. $$\dfrac{b^2-a^2}{2}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Medium
$$\displaystyle \int _{ 0 }^{ \pi /4 }{ \tan ^{ 2 }{ x } dx= } $$
  • A. $$1+\dfrac {\pi}{4}$$
  • B. $$\dfrac {-\pi}{4}-1$$
  • C. $$\dfrac {\pi}{4}-1$$
  • D. $$1-\dfrac {\pi}{4}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Medium
If  $$\displaystyle \int_{0}^{k}\frac{\cos x}{1+\sin^{2}x}dx=\frac{\pi}{4}$$ then $${k}=?$$
  • A. $$1$$
  • B. $$\pi/4$$
  • C. $$\pi/6$$
  • D. $$\pi/2$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Passage Hard

In calculating a number of integrals we had to use the method of integration by parts several times in succession. The result could be obtained more rapidly and in a more concise form by using the so-called generalized formula for integration by parts. 

$$\int u(x)\, v(x)dx\, =\, u(x)\, v_{1}(x)\, -\, u^{}(x)v_{2}(x)\, +\, u^{}(x)\, v_{3}(x)\, -\, .\, +\, (-1)^{n\, -\, 1}u^{n\, -\, 1}(x)v_{n}(x)\, -\, (-1)^{n\, -\, 1}$$ $$\int\, u^{n}(x)v_{n}(x)\, dx$$ where $$v_{1}(x)\, =\, \int v(x)dx,\, v_{2}(x)\, =\, \int v_{1}(x)\, dx\, ..\, v_{n}(x)\, =\, \int v_{n\, -\, 1}(x) dx$$

Of course, we assume that all derivatives and integrals appearing in this formula exist. The use of the generalized formula for integration  by parts is especially useful when calculating $$\int P_{n}(x)\, Q(x)\, dx$$, where $$P_{n}(x)$$, is polynomial of degree n and the factor Q(x) is such that it can be integrated successively n + 1 times.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer