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NDA Exam Mathematics Study Material

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Integration and Differential Equations

When derivative of a function is given and we have to determine the function, this process is called _________ .

a) Derivation
b) Integration
c) Limits
d) Differentiation

✔Answer

Correct Answer Is : Integration

Solution Is :

The integration is the inverse process of a ____________.

a) Differentiation
b) Limits
c) Applications of integration
d) Applications of differentiation

✔Answer

Correct Answer Is : Differentiation

Solution Is :

If∫ f (x)dx, f(x) is?

a) An integral
b) Derivative
c) Any function
d) All of these

✔Answer

Correct Answer Is : An integral

Solution Is :

If∫ f (x)dx, f(x) is an integral and x is ?

a) A constant variable
b) A variable of integral
c) A variable of constant
d) A integration function

✔Answer

Correct Answer Is : A variable of integral

Solution Is :

If a and b are any non-zero real number,∫(1/(ax + b))dx = ?

a) Log |ax + b|/a + c
b) Log |ax + b|/a
c) Log |ax + b|/b + c
d) Log |ax - b|/a + c

✔Answer

Correct Answer Is : Log |ax + b|/a + c

Solution Is :

If a and b are any non-zero real number,∫cos (ax + b)dx = ?

a) Sin (ax + b) /a
b) Sin (ax + b) /a + c
c) Sin (ax - b) /a
d) Sin (ax - b) /a + c

✔Answer

Correct Answer Is : Sin (ax + b) /a + c

Solution Is :

True or false: integral is also called anti-derivative.

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

✔Answer

Correct Answer Is : TRUE

Solution Is :

If a and b are any non-zero real number,∫(e^(ax + b))dx = ?

a) E^(ax + b)
b) E^(ax + b)/a
c) E^(ax + b)/a + c
d) All of these

✔Answer

Correct Answer Is : E^(ax + b)/a + c

Solution Is :

If a and b are any non-zero real number,∫(sin(ax + b))dx = ?

a) (-cos(ax + b))
b) (cos(ax + b))
c) (-cos(ax + b))/a
d) (-cos(ax + b))/a + c

✔Answer

Correct Answer Is : (-cos(ax + b))/a + c

Solution Is :

If f(x) and g(x) are two real value functions such that∫ f(x)dx and∫ g(x)dx exist, then

a) ∫[f(x) ± g(x)]dx =∫ f(x)dx ±∫ g(x)dx
b) ∫[f(x) ± g(x)]dx =∫ f(x)dx +∫ g(x)dx
c) ∫[f(x) ± g(x)]dx =∫ f(x)dx -∫ g(x)dx
d) All of these

✔Answer

Correct Answer Is : All of these

Solution Is :

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NDA Exam Mathematics Study Material

Integration and Differential Equations

When derivative of a function is given and we have to determine the function, this process is called _________ .

Correct Answer Is : Integration

Solution Is :

The integration is the inverse process of a ____________.

Correct Answer Is : Differentiation

Solution Is :

If∫ f (x)dx, f(x) is?

Correct Answer Is : An integral

Solution Is :

If∫ f (x)dx, f(x) is an integral and x is ?

Correct Answer Is : A variable of integral

Solution Is :

If a and b are any non-zero real number,∫(1/(ax + b))dx = ?

Correct Answer Is : Log |ax + b|/a + c

Solution Is :

If a and b are any non-zero real number,∫cos (ax + b)dx = ?

Correct Answer Is : Sin (ax + b) /a + c

Solution Is :

True or false: integral is also called anti-derivative.

Correct Answer Is : TRUE

Solution Is :

If a and b are any non-zero real number,∫(e^(ax + b))dx = ?

Correct Answer Is : E^(ax + b)/a + c

Solution Is :

If a and b are any non-zero real number,∫(sin(ax + b))dx = ?

Correct Answer Is : (-cos(ax + b))/a + c

Solution Is :

If f(x) and g(x) are two real value functions such that∫ f(x)dx and∫ g(x)dx exist, then

Correct Answer Is : All of these

Solution Is :

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