Indefinite Integrals MCQ Quiz in मल्याळम - Objective Question with Answer for Indefinite Integrals - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

The correct answer is option '1'.

Concept:

Indefinite integral:

• An indefinite integral is the integration of a function without limits.
• Integration is the reverse process of differentiation.
• Integration is defined for a function f(x) and it helps in finding the area enclosed by the curve, with the reference to one of the coordinate axes.

Calculation:

Integration of e^kx 

Integrating f (x) = ekx with respect to dx.

where 'c' is the constant,

Concept:

For Integration with modulus, first we have to find the point where the sign of the value of the function gets change.

Calculation:

Given:

f(x) = 5x - 3 = 0

x = 3/5

∴ from 0 to 3/5 the function is negative and 3/5 to 1 the function is positive.

Concept:

For Integration with modulus, first we have to find the point where the sign of the value of the function gets change.

Calculation:

Given:

f(x) = 5x - 3 = 0

x = 3/5

∴ from 0 to 3/5 the function is negative and 3/5 to 1 the function is positive.

Let,

By solving through integration by parts, we get

where C is constant

has real roots and

So from case III: or

Given
We need to evaluate the integral ∫sin(√x/√/x)dx

Formula Used
using the Substitution method for integration.

Calculation:
∫ sin  dx 

⇒ Put √x = t

⇒  = dt 

⇒  

 sin  dx = 2 ∫ sin t dt = -2 cost + c = -2 cos(√x) + c

Hence, The Correct Answer is Option 3.

Explanation:

 is not true for n = -1

because for n = -1

 =  = log |x| + c

(5) is correct

Explanation:

Let I = 

 ⇒ I = 

Let 2x + 3 = t ⇒ 2 dx = dt  

dx = 

⇒ I = 

⇒ l=  

⇒ I = 

⇒ I = 

⇒ I = 

⇒ I = 

⇒ I =  

⇒ I =  +  +C

⇒ I =  +  + C

⇒ I =   +  +C

⇒ I =   +   +C

⇒ I=   [ ]+C  

Substitute t = 2x + 3 in the above equation, we have

⇒ I =  [ ] +C

⇒ I =  [  ] +C

⇒  =  [] +C

Hence, the correct answer is option (3).

Given that,

     ----(1)

We know that,

      ----(2)

      ----(3)

Now, equation (1) can be written as

By substituting equation (2) and (3) in the above equation