int(0)^(2a)f(x)dx-int(0)^(a)f(x)dx=...

`int_(0)^(2a)f(x)dx-int_(0)^(a)f(x)dx=`

`int_(0)^(a)f(x)dx`

`int_(0)^(a)f(2a-x)dx`

`int_(0)^(a)f(a-2x)dx`

`int_(0)^(a)f(a+2x)dx`

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If int_(0)^(2a) f(x)dx=int_(0)^(2a) f(x)dx , then

If : int_(0)^(2a)f(x)dx=2.int_(0)^(a)f(x)dx , then :

STATEMENT 1: The value of int_(0)^(2 pi)cos^(99)xdx is 0 STATEMENT 2:int_(0)^(2a)f(x)dx=2int_(0)^(a)f(x)dx, if f(2a-x)=f(x)

Prove the following properties of definite integrals : int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx

Prove that int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx

Statement-1: int_(0)^(pi//2) (1)/(1+tan^(3)x)dx=(pi)/(4) Statement-2: int_(0)^(a) f(x)dx=int_(0)^(a) f(a+x)dx

Prove that: int_(0)^(2a)f(x)dx=int_(0)^(2a)f(2a-x)dx

Let f(x) and g(x) be any two continuous function in the interval [0, b] and 'a' be any point between 0 and b. Which satisfy the following conditions : f(x)=f(a-x), g(x)+g(a-x)=3, f(a+b-x)=f(x) . Also int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx, int_(a)^(b)f(x)dx=int_(a)^(b)f(x)dx=int_(a)^(b)f(a+b-x)dx If int_(0)^(a//2)f(x)dx=p," then "int_(0)^(a)f(x)dx is equal to

STATEMENT-1 : int_(0)^((pi)/(2))(xsinxcosx)/(sin^(4)x+cos^(4)x)dx=(pi^(2))/(32) and STATEMENT-2 : int_(0)^(a)f(x)dx=int_(0)^(a)f(a-x)dx

Property 6: If f(x) is a continuous function defined on [0;2a] then int_(0)^(2)a=int_(0)^(a)f(x)dx+int_(0)^(a)f(2a-x)dx

MARVEL PUBLICATION-INTEGRATION - DEFINITE INTEGRALS -MULTIPLE CHOICE QUESTIONS (PART - B : Mastering The BEST)

int(1)^(e )((log x)^(3))/(x)dx=
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int(1)^(3)(1)/(sqrt(4x-x^(2)-3))dx=
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int(0)^(2a)f(x)dx-int(0)^(a)f(x)dx=
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int(0)^(pi)(cos^(4)x-sin^(4)x)dx=
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If int(0)^(pi//2)sin^(4)x cos^(2)x dx=(pi)/(32), then int(0)^(pi//2)si...
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int(0)^(pi//4)sqrt((1-sin2x)/(1+sin 2x))dx=
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int(0)^(pi//2)(cos x)/(1+sin^(2)x)dx=
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Evaluate : int(-pi/2)^(pi/2)(cosx)/(1+e^x)dx
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int(sqrt(2)//3)^(sqrt(3)//3)(1)/(sqrt(4-9x^(2)))dx=
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Evaluate : int0^1sqrt(x(1-x))dx
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int(0)^(1)(1)/(x+sqrt(x))dx=
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int(0)^(pi//4)(sin^(9)x)/(cos^(11)x)dx=
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int(0)^(pi//4)(tan^(4)x + tan^(2)x)dx=
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int(2)^(3)(1)/(x^(2)-x)dx=
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int(0)^(3)(x+1)/(x^(2)+9)dx=
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If int(0)^(pi)x f(sin x) dx = a int(0)^(pi)f (sin x) dx, then a =
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int(0)^(pi//2)(1)/(1+tan^(3)x)dx=
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Evaluate int0^1 tan^(-1) (1/(1-x+x^2)) dx
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If 2int0^1 tan^(-1)x dx= int0^1 cot^(-1)(1-x+x^2) dx then int0^1 tan^(...
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int(0)^(pi)(e^(cos x))/(e^(cos x)+e^(-cos x))dx=
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