Mathematics

$$\displaystyle \int_{\pi/4}^{\pi/4} ln \sqrt{1+\sin2x}dx$$ dx has the value equal to:


ANSWER

$$\dfrac{\pi}{4}\ln2$$


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

If $$f(x)=\displaystyle \frac{e^{x}}{1+e^{x}}$$ ,$$I_{1}=\displaystyle \int_{f(-a)}^{f(a)}xg\{x(1-x)\}dx $$ and $$I_{2}=\displaystyle \int_{f(-a)}^{f(a)}g\{x(1-x)\}dx$$, then the value $$\displaystyle \frac{I_{2}}{I_{1}} $$ is
  • A. -3
  • B. -1
  • C. 1
  • D. 2

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q2 Subjective Hard
Integrate      
$$\int {\frac{{2\sin 2x - \cos x}}{{6 - {{\cos }^2}x - 4{\mathop{\rm sinx}\nolimits} }}dx} $$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q3 Single Correct Hard
$$\int \cos(\ln x)dx=$$
  • A. $$\dfrac{x}{2}[\cos \ln x-\sin \ln x]$$
  • B. $$[x \cos \ln x + \sin \ln x]$$
  • C. None of these
  • D. $$\dfrac{x}{2}(\cos \ln x+\sin \ln x)$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q4 Single Correct Hard
If $$\displaystyle \int_{1}^{x}\dfrac{dt}{|t|\sqrt{t^{2}-1}}=\dfrac{\pi}{6}$$, then $$x$$ can be equal to :
  • A. $$\sqrt{3}$$
  • B. $$2$$
  • C. $$\dfrac{4}{\sqrt{3}}$$
  • D. $$\dfrac{2}{\sqrt{3}}$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer
Q5 Subjective Easy
$$\int(2x^2-3 \, sin x+5 \sqrt{x})dx$$

Asked in: Mathematics - Integrals


1 Verified Answer | Published on 17th 09, 2020

View Answer