Mathematics

$$\displaystyle \int \frac{co\sec^{2}x-203}{\left ( \cos x \right )^{203}}dx$$


ANSWER

$$\displaystyle \frac{-\cot x}{\left ( \cos x \right )^{203}}$$


SOLUTION
$$\displaystyle \int \left ( \cos^{-203} x\right )co\sec^{2}xdx-\int \frac{203}{\left ( \cos x \right )^{203}}dx$$
$$\displaystyle =I_{1}-I_{2}$$
Integrate $$\displaystyle I_{1}$$ by parts
$$\displaystyle

\therefore I_{1}=\left ( \cos ^{-203}x \right )\left ( -\cot x \right

)-\int \cot x.203\cos ^{-204}x\left ( -\sin x \right )dx$$
$$\displaystyle

I_{1}=-\frac{\cot x}{\left ( \cos x \right )^{203}}+\int \frac{203}{\left (

\cos x \right )^{203}}dx +C$$
$$\displaystyle \therefore I_{1}-I_{2}=-\frac{\cot x}{\left ( \cos x \right )^{203}}+C$$
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 114
Enroll Now For FREE

Realted Questions

Q1 Subjective Medium
Show that $$\displaystyle I= \int_{0}^{\pi }\dfrac{xdx}{a^{2}\cos ^{2}x+b^{2}\sin ^{2}x}= \dfrac{\pi }{2ab}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Medium
$$\int _{ 1 }^{ 3 }{ a^{ x } } dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Medium

Evaluate the following definite integral:
$$\displaystyle \int^{\pi /4}_{-\pi /4}\log(\cos x+\sin x)dx$$
  • A. $$\pi$$ log2
  • B. $$-\pi$$ log2
  • C. $$\pi^{2}\log 2$$
  • D. $$-\displaystyle \frac{\pi}{4} \log 2$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Hard
Given that for each $$\displaystyle a  \in (0, 1), \lim_{h \rightarrow 0^+} \int_h^{1-h} t^{-a} (1 -t)^{a-1}dt$$ exists. Let this limit be $$g(a)$$ 
In addition, it is given that the function $$g(a)$$ is differentiable on $$(0, 1)$$, then The value of $$g'(\frac{1}{2})$$ is?
  • A. $$\displaystyle \frac{\pi}{2}$$
  • B. $$\pi$$
  • C. $$\displaystyle -\frac{\pi}{2}$$
  • D.

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Passage Medium
Let $$\displaystyle I_{1}=\int_{0}^{1}(1-x^{2})^{1/3} dx$$  &  $$\displaystyle I_{2}=\int_{0}^{1}(1-x^{3})^{1/2} dx$$

On the basis of above information, answer the following questions: 

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer