Aof Panel

Soru 1

What is the antiderivative of the indefinite integral ∫ x²/4 dx?

Soru 2

I. A function F is called an antiderivative of f on an interval (a, b) if F' (x) = f (x) for all x in (a, b).

II. The family of all antiderivatives of a function f, F(x)+ c is called the indefinite integral of f.

III. The process of finding antiderivatives of a given function is called derivation.

What can be said to be true about indefinite integrals?

Soru 3

From the fundamental rules of integration which is the rule that states

?

Soru 4

I. In the substitution method we change the variable of the integrand to something more convenient, or to put it more correctly, to a form where the previous rules may be applied directly.

II. This method is usually applied if a certain part of the integrand can be viewed as the derivative of remaining part of the integrand.

III. After integrating with respect to the new variable, it is not necessary to “back substitute” and getting the integral back in terms of the original variable.

What can be said to be true about the Change of Variable Method (Substitution Method)?

Soru 5

I. The integration by parts method is derived from the differentiation rule of the product of any two functions.

II. In the method of integration by parts, first we need to choose u and v. Then, we find du and dv and then we write all of these results.

III. Once we have taken the last integral in the problem, we will add in the constant of integration c to get our final answer.

What can be said to be true about integration by parts?

Soru 6

What is the antiderivative of ∫ 2 lnx dx equal to?

Soru 7

What is the equation used in the intagration by parts method?

Soru 8

What is the antiderivative of the integral ∫ 2.e^x+4.dx value equal to?

Soru 9

I. ∫kdx = kx + c

II. ∫x^rdx = x^{r -1}/r - 1 + c

III. ∫1/x .dx = lnx +c , x>0

Which of the given basic rule can be said to be true?

Soru 10

What is the antiderivative of the integral ∫ 2.e^2x+ (2x² - 4x + 1).dx value equal to?

Soru 11

Which of the following functions is an antiderivative of

Soru 12

Which of the following is the function satisfying

and F(0)=2?

Soru 13

What is the result of

Soru 14

What is the result of

Soru 15

What is the result of ∫(x+2)e^x-8dx?

Soru 16

What is the result of

Soru 17

What is the result of ∫x²ln(x²)dx?

Soru 18

What is the result of

Soru 19

Soru 20

Find the integral

MATHEMATICS II