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Applications of the Integrals

If f(x) is a continuous function of x, then exists a function ɸ(x) such that _________ .

a) ɸ(x) = f(x)
b) ɸ (x) = f(x)
c) ɸ(x) = f (x)
d) ɸ (x) = f (x)

✔Answer

Correct Answer Is : ɸ (x) = f (x)

Solution Is :

If we restrict domain of x to (a,b), then the difference ɸ(b) - ɸ(a) is called ___________ .

a) Integration
b) Definite integral
c) Differentiation
d) All of these

✔Answer

Correct Answer Is : All of these

Solution Is :

If ∫f(x)dx = ɸ(x) + c , then (integration a to b)f(x)dx =

a) ɸ(x)
b) ɸ(b) - ɸ(a)
c) ɸ(a) - ɸ(b)
d) ɸ(b) + ɸ(a)

✔Answer

Correct Answer Is : ɸ(b) + ɸ(a)

Solution Is :

True or false: in definite integrals there is no need of taking the constant of integration.

a) TRUE
b) FALSE
c) MAYBE
d) None of these

✔Answer

Correct Answer Is : MAYBE

Solution Is :

Evaluate: (integration 0 to 4) (1 / (√(4x- x^2)).dx

a) Π
b) Π / 2
c) Π / 4
d) Π / 6

✔Answer

Correct Answer Is : Π / 4

Solution Is :

The area of the portion lying above the ____________ is positive.

a) X-axis
b) Y-axis
c) Dependent on assumption
d) None of these

✔Answer

Correct Answer Is : Dependent on assumption

Solution Is :

True or false: (integration 0 to (Π / 4 )) sin^4 x.dx is 3Π.

a) TRUE
b) FALSE
c) MAYBE
d) None of these

✔Answer

Correct Answer Is : None of these

Solution Is :

Evaluate: (integration 0 to 1) (1 / (2x + 5)).dx

a) (1/2) log (7/5)
b) Log (7/5)
c) -1
d) -1

✔Answer

Correct Answer Is : -1

Solution Is :

Find the volume of sphere of radius 6.

a) 288 cubic units
b) 288Π cubic units
c) 88Π cubic units
d) 28Π cubic units

✔Answer

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Class 12 Maths Study Material

Applications of the Integrals

If f(x) is a continuous function of x, then exists a function ɸ(x) such that _________ .

Correct Answer Is : ɸ (x) = f (x)

Solution Is :

If we restrict domain of x to (a,b), then the difference ɸ(b) - ɸ(a) is called ___________ .

Correct Answer Is : All of these

Solution Is :

If ∫f(x)dx = ɸ(x) + c , then (integration a to b)f(x)dx =

Correct Answer Is : ɸ(b) + ɸ(a)

Solution Is :

True or false: in definite integrals there is no need of taking the constant of integration.

Correct Answer Is : MAYBE

Solution Is :

Evaluate: (integration 0 to 4) (1 / (√(4x- x^2)).dx

Correct Answer Is : Π / 4

Solution Is :

The area of the portion lying above the ____________ is positive.

Correct Answer Is : Dependent on assumption

Solution Is :

True or false: (integration 0 to (Π / 4 )) sin^4 x.dx is 3Π.

Correct Answer Is : None of these

Solution Is :

Evaluate: (integration 0 to 1) (1 / (2x + 5)).dx

Correct Answer Is : -1

Solution Is :

Find the volume of sphere of radius 6.

Correct Answer Is : 28Π cubic units

Solution Is :

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