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"If " int f(x)dx=Psi(x), " then " int x^...

` "If " int f(x)dx=Psi(x), " then " int x^(5)f(x)^(3)dx " is equal to "`

A

` (1)/(3) [ x ^3 Psi (x ^ 3 ) - int x ^ 2 Psi (x^3 ) dx ] + C `

B

` (1)/(3) x ^ 3 Psi ( x ^ 3 ) - 3 int x ^3 Psi (x ^ 3 ) dx + c `

C

` (1)/(3) x ^ 3 Psi (x ^3) - int x ^2 Psi (x ^3 ) dx + c `

D

` (1)/(3) [ x ^3 Psi (x^3 ) - int x ^3 Psi (x^3 ) dx ] + c `

Text Solution

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The correct Answer is:
C
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VMC MODULES ENGLISH-INTEGRAL CALCULUS-1-JEE MAIN (ARCHIVE)
  1. The value of int1/(x^(2)(x^(4)+1)^(3//4)) dx is equal to

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  2. "The integral " int(1+x-(1)/(x))e^(x+(1)/(x))dx " is equal to "

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  3. "If " int f(x)dx=Psi(x), " then " int x^(5)f(x)^(3)dx " is equal to "

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  4. Evaluate:int \ (sin^2x cos^2x)/(sin^5x+cos^3x sin^2x + sin^3x cos^2x +...

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  5. if f ((x- 4 ) /(x + 2 )) = 2 x + 1 , (x in R - { 1, - 2 }) , ...

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  6. If int (2x + 5 )/(sqrt(7 - 6 x - x ^ 2 )) dx = A sqrt (7 - ...

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  7. The value of int (tan x )/(tan ^(2) x + tan x+1)dx =x -(2)/(sqrtA) tan...

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  8. The value of int(-pi//2)^(pi//2)(sin^(2)x)/(1+2^(x))dx is

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  9. The value of the integral int(0) ^(pi//2) sin ^3 x dx is :

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  10. The value of int(pi//4)^(3pi//4)(x)/(1+sin x)dx ….

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  11. if x^(2) !=npi+1, ninN then int x sqrt((2sin(x^(2)-1)-sin2(x^(2)-1))/(...

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  12. If f(x)=int(5x^8+7x^6)/((x^2+1+2x^7))dx,(xge0)andf(0)=0, then the valu...

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  13. Let nge2 be a natural number and 0ltthetaltpi//2. Then int((sin^ntheta...

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  14. If intx^5e^(-4x^3)dx=(1)/(48)e^(-4x^3)(f(x))+c, where c is contant of ...

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  15. If int(sqrt(1-x^2))/x^4dx=A(x) (sqrt(1-x^2))^m+C,for a suitable chose...

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  16. If int (x+1)/(sqrt(2x-1))dx=f(x) sqrt(2x-1)+C, where C is a constant o...

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  17. The integral intcos(logex)dx is equal to (where C is a contant of int...

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  18. The integral int(3x^13+2x^11)/((2x^4+3x^2+1)^4)dx is equal to (where C...

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  19. int("sin"(5x)/(3))/("sin"(x)/(2))dx is equal to (where, C is a constan...

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  20. "If"int(dx)/(x^(3)(1+x^(6))^(2/3))=xf(x)(1+x^(6))^(1/3)+C where, C is ...

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