∫ π 2 0 s i n 2 x c o s 3 x d x = [RPET 1984, 2003] Options: A . &nbsp0 B . &nbsp215 C . &nbsp415 D . &nbspNone of these

Answer: Option B : B Using gamma function, ∫ π 2 0 s i n 2 x c o s 3 x d x = r ( 3 2 ) r 2 2 r ( 7 2 ) = 2 15

∫π20 sin2x cos3x dx= [RPET 1984, 2003]

Question

\int_{0}^{\frac{π}{2}} s i n^{2} x c o s^{3} x d x =

[RPET 1984, 2003]

Options:

A . 0

B . 215

C . 415

D . None of these

Answer: Option B
:
B
Using gamma function,

\int_{0}^{\frac{π}{2}} s i n^{2} x c o s^{3} x d x = \frac{r (\frac{3}{2}) r 2}{2 r (\frac{7}{2})} = \frac{2}{15}

Was this answer helpful ?

Next Question

Question 1. Antiderivative of all the continuous functions can be written in terms of elementary functions....

Question 2. If a function f(x) is discontinuous in the interval (a,b) then ∫baf(x)dx never exists.....

Question 3. ∫∞11x2dx does not have a finite value....

Question 4. Let f be a positive function. Let I1=∫k1−k xf{x(1−x)}dx, I2=∫k1−....f be a positive function. Let I1=∫k1−k xf{x(1−x)}dx, I2=∫k1−kf{x(1−x)}dx when 2k−1>0. Then I1I2 is [IIT 1997 Cancelled]

Question 5. ∫π2−π2 sin2x dx=....

Question 6. Find the integral ∞∫0e−xdx.....

Question 7. ∫π20 log(tan x+cot x)dx=....

Question 8. ∫10π0|sin x|dx is....

Question 9. Calculate ∫3−2f(x)dx wheref(x)={6ifx>13x2ifx≤1 ....

Question 10. Limπ→∞199+299+399+⋯⋯n99n100= [EAMCET 1994]....

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0