# Which statement below is considered to be a correct

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5. (10 points) Which statement below is considered to be a correct version of the Fun- damental Theorem of Calculus? Put the letter of the correct answer in the provided box. A: Assume f ( x ) is a continuous function on [ a, b ]. Then d dx x Z a f ( t ) dt = f ( x ) B: Assume f ( x ) is a continuous function on [ a, b ]. Then d dx a Z x f ( t ) dt = f ( x ) C: Assume f ( x ) is a continuous function on [ a, b ] and a < c < b . Then c Z a f ( x ) dx + b Z c f ( x ) dx = b Z a f ( x ) dx D: Assume f ( x ) is a continuous function on [ a, b ]. Then b Z a f ( x ) dx = lim n →∞ n X j =1 f ( c j x where Δ x = b - a n , c j = a + i Δ x . 6. (10 points) Evaluate dx after giving the completed partial fraction
x ( x 2 + 2 x + 3) decomposition (PFD) of the integrand (i.e. include the values of the constants in the numerators). PFD (WITH values of the coefficients) = Evaluated Integral = 2
7. (15 points) Let R be the region between the graph of the function y = x 2 and the y -axis where 0 x 1. Let V be the volume of the solid obtained by rotating the region R about the y -axis. (a) Find a formula for V using the washer method and put the letter of the correct answer in the provided box.
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