Select Goal &
City
Select Goal
Explore
Question:
If \(f(x) + f(\pi-x) = \pi^{2}\) then \(_{0}\int^{\pi}f(x) sinx dx\) ?
If \(f(x) + f(\pi-x) = \pi^{2}\) then \(_{0}\int^{\pi}f(x) sinx dx\) ?
Updated On: Aug 21, 2024
- π2
- \(\frac{\pi_2}{4}\)
- 2π2
- \(\frac{\pi_2}{8}\)
Hide Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
The correct option is (A): π2
\(I=\int_0^\pi f(x)sinxdx\)
\(I=\int_0^\pi f(\pi-x)sinxdx\)
\(2I=\int_0^\pi sin(x)(f(x)+f(\pi-x))dx\)
\(2I=\pi^2\int_0^\pi sinxdx\)
\(2I=2\pi^2\int_0^\pi sinxdx\)
\(I=\pi^2(-cos x)^\frac{\pi}{2}_0\)
\(I=\pi^2\)
\(I=\int_0^\pi f(x)sinxdx\)
\(I=\int_0^\pi f(\pi-x)sinxdx\)
\(2I=\int_0^\pi sin(x)(f(x)+f(\pi-x))dx\)
\(2I=\pi^2\int_0^\pi sinxdx\)
\(2I=2\pi^2\int_0^\pi sinxdx\)
\(I=\pi^2(-cos x)^\frac{\pi}{2}_0\)
\(I=\pi^2\)
Was this answer helpful?
0
0
Top Questions on Integration by Parts
- \(∫xlog(1+x^2)dx=\)?
- KEAM - 2023
- Mathematics
- Integration by Parts
- If $\int\limits_0^1\left(x^{21}+x^{14}+x^7\right)\left(2 x^{14}+3 x^7+6\right)^{1 / 7} d x=\frac{1}{l}(11)^{m / n}$ where $l, m, n \in N , m$ and $n$ are coprime then $l+m+n$ is equal to ______
- JEE Main - 2023
- Mathematics
- Integration by Parts
- \(∫_0^1 (5xe^{2x}-tan(π/4)) dx=\)
- KEAM - 2023
- Mathematics
- Integration by Parts
- If I=∫\(\frac{x^2dx}{(x\,sin\,x+cos\,x)^2}\)=f(x)+tan x+c, then f(x) is
- WBJEE - 2023
- Mathematics
- Integration by Parts
the value of ∫cot2xdx is________________
- SRMJEEE - 2023
- Mathematics
- Integration by Parts
View More Questions
Questions Asked in JEE Main exam
- Let \[\vec{a} = \hat{i} + \hat{j} + \hat{k}, \quad \vec{b} = -\hat{i} - 8\hat{j} + 2\hat{k}, \quad \text{and} \quad \vec{c} = 4\hat{i} + c_2\hat{j} + c_3\hat{k} \]be three vectors such that \[\vec{b} \times \vec{a} = \vec{c} \times \vec{a}.\]If the angle between the vector $\vec{c}$ and the vector $3\hat{i} + 4\hat{j} + \hat{k}$ is $\theta$, then the greatest integer less than or equal to $\tan^2 \theta$ is:
- JEE Main - 2024
- Vector Algebra
- 10 mL of gaseous hydrocarbon on combustion gives 40 mL of CO\(_2\)(g) and 50 mL of water vapour. The total number of carbon and hydrogen atoms in the hydrocarbon is ______ .
- JEE Main - 2024
- Hydrocarbons
- If each term of a geometric progression \( a_1, a_2, a_3, \dots \) with \( a_1 = \frac{1}{8} \) and \( a_2 \neq a_1 \), is the arithmetic mean of the next two terms and \( S_n = a_1 + a_2 + \dots + a_n \), then \( S_{20} - S_{18} \) is equal to
- JEE Main - 2024
- Arithmetic Mean
A body of mass 1000 kg is moving horizontally with a velocity of 6 m/s. If 200 kg extra mass is added, the final velocity (in m/s) is:
- JEE Main - 2024
- speed and velocity
- $\textbf{Choose the correct statements about the hydrides of group 15 elements.}$
A. The stability of the hydrides decreases in the order \(\text{NH}_3 > \text{PH}_3 > \text{AsH}_3 > \text{SbH}_3 > \text{BiH}_3\)
B. The reducing ability of the hydrides increases in the order \(\text{NH}_3 < \text{PH}_3 < \text{AsH}_3 < \text{SbH}_3 < \text{BiH}_3\)
C. Among the hydrides, \(\text{NH}_3\) is a strong reducing agent while \(\text{BiH}_3\) is a mild reducing agent.
D. The basicity of the hydrides increases in the order \(\text{NH}_3 < \text{PH}_3 < \text{AsH}_3 < \text{SbH}_3 < \text{BiH}_3\)
Choose the most appropriate from the option given below:- JEE Main - 2024
- p -Block Elements
View More Questions
Concepts Used:
Integration by Parts
Integration by Parts is a mode of integrating 2 functions, when they multiplied with each other. For two functions ‘u’ and ‘v’, the formula is as follows:
∫u v dx = u∫v dx −∫u' (∫v dx) dx
- u is the first function u(x)
- v is the second function v(x)
- u' is the derivative of the function u(x)
The first function ‘u’ is used in the following order (ILATE):
- 'I' : Inverse Trigonometric Functions
- ‘L’ : Logarithmic Functions
- ‘A’ : Algebraic Functions
- ‘T’ : Trigonometric Functions
- ‘E’ : Exponential Functions
The rule as a diagram:
SUBSCRIBE TO OUR NEWS LETTER
COLLEGE NOTIFICATIONSEXAM NOTIFICATIONSNEWS UPDATES
Download the Collegedunia app on 
© 2024 Collegedunia Web Pvt. Ltd. All Rights Reserved