Question:
The value of
\[
\int_0^{\frac{\pi}{2}} \sin^7 \theta \cos^4 \theta \, d\theta
\]
is
The value of
\[
\int_0^{\frac{\pi}{2}} \sin^7 \theta \cos^4 \theta \, d\theta
\]
is
Show Hint
For integrals involving powers of trigonometric functions, use reduction formulas or standard integral tables for simplification.
Updated On: Dec 11, 2025
- \( \frac{16}{1155} \)
- \( \frac{16}{115} \)
- \( \frac{385}{1155} \)
- \( \frac{385}{16\pi} \)
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The integral is evaluated using standard trigonometric integral techniques, leading to the result \( \frac{16}{1155} \).
Was this answer helpful?
0
0
Top IPU CET Mathematics Questions
- Choose the most appropriate options.
\[ \int \frac{x^2 - 2}{x \sqrt{x^2 - 1}}\,dx \text{ equal to} \] - \[ \lim_{x \to 0} \frac{\sqrt{1+x} - \sqrt{1 - x}}{x} \]
- In how many ways can the four walls of a room be painted with three colours such that no two adjacent walls have the same colour?
- A die is thrown twice and the sum of the numbers appearing is 6. Then, the conditional probability that the number 4 has appeared at least once is
- There are 3 true coins and 1 false coin with 'head' on both sides. A coin is chosen at random and tossed 4 times. If 'head' occurs all the 4 times, then the probability that the false coin has been chosen and used is
View More Questions
Top IPU CET Integration Questions
- Choose the most appropriate options.
\[ \int \frac{x^2 - 2}{x \sqrt{x^2 - 1}}\,dx \text{ equal to} \] - \[ \int_{-\pi/2}^{\pi/2} |\sin x| dx \text{ equals to} \]
- \[ \int \frac{x^2}{(x \sin x + \cos x)^2} dx \text{ is equal to} \]
- \[ \int_0^1 x e^{2x} dx \text{ is equal to} \]
- \[ \int_{-1}^1 \frac{x \sin^{-1} x}{\sqrt{1 - x^2}} dx \text{ is equal to} \]
View More Questions
Top IPU CET Questions
- The two kinds of main memory are:
- In computer terminology, what is the full form of RAM?
- Permanent instructions that the computer use when it is turned ON and are not changed by other instructions are contained in:
- What is the full form of PROM?
- Which of the following acts as a buffer between the CPU and the main memory?
View More Questions