Mathematics 2

Yanıt Açıklaması: The sought for area A is expressed in terms of the definite integral as Let and we get and With these results inserted in the integration by parts rule we obtain The correct answer is E.

Yanıt Açıklaması: This is a Euler equation so we start from the trial solution Then we get and Substituting these results into the ODE, we obtain the equation in the form So, the general solution is The correct answer is C.

Yanıt Açıklaması: Since and since Thus upper sum of  corresponding to the given partition is

Yanıt Açıklaması: Thus lower sum of  corresponding to given partition is

Yanıt Açıklaması: The antiderivative of the integrand is Therefore the correct answer is the B option.

Yanıt Açıklaması: Given parabola intersects the and The area of the region corresponding to the interval equals to the area corresponding to Hence required area  is calculated by the definite integral Because we observe that and Thus, we get The right answer is B.

Yanıt Açıklaması: Therefore the correct answer is the E option.

Yanıt Açıklaması: the correct answer is A.

Yanıt Açıklaması: From the linearity of the integral, we find

Yanıt Açıklaması: Observe that for any arbitrary real number c.

Yanıt Açıklaması: Then the solution can be written as If we use the initial condition we get that Thus, we can write the solution as: Thus, the correct answer is D.

Yanıt Açıklaması: Since which is given in the graph, the required answer is found as Therefore the correct answer is the B option.

Yanıt Açıklaması: As before, we only need to apply the formula for the future value of an income. Since the time period is T = 4 and the interest rate gives r = 0,25, we have Therefore the correct answer is the B option.

Yanıt Açıklaması: Correct answer is E .

Yanıt Açıklaması: We need the intersection points of given curves: Hence, we have to evaluate the definite integral on the interval Therefore required area  is evaluated as that means the right answer is A.

Yanıt Açıklaması: on the interval and since the function is even the area A can be calculated by definite integral: Calculating the integral gives the area as Hence the correct answer is C.

Yanıt Açıklaması: Hence the correct solution is E.