MATHEMATICS II - Deneme Sınavı - 3

The characteristic equation ⇒ . The general solution .

Integrating factor  Integrating by parts 

Therefore, the general solution is . From initial condition y(0)=-2, hence -2=C+1/2⇒ C=-5/2
Thus, the solution .

 Integrating factor 

 The general solution  

Therefore the correct answer is the D option.

Therefore the correct answer is the B option.

then

Therefore the correct answer is the C option.

Therefore the correct answer is the E option.

Therefore the correct answer is the B option.

Therefore the correct answer is the C option.

Therefore the correct answer is the B option.

on the interval [-2, 1], therefore the sought for area A can be calculated by definite integral:

The antiderivative of 

is

so 

Therefore the correct answer is the C option.

Therefore the correct answer is the B option.

Therefore the correct answer is the E option.

we get,

Returning back to the original variable x, we find that the antiderivative of f is

. Thus, the definite integral is

Therefore the correct answer is the D option.

Therefore the correct answer is the E option.

Therefore the correct answer is the D option.

The points satisfying the last equation are -2, 0, 2. Since there is an extra condition of x≥0, the points
of intersection are 0 and 2. Also, in the interval 0≤x≤2, we have 

and therefore the required area A is evaluated as

Therefore the correct answer is the C option.