6 calculus questions

Which of the following definite integrals represents the area of the shaded region? a ) [(4 - x2) dx b ) [ ( 4 - x2 ) dx y = 4 - x 2 0 2 c ) [ (4 - x2) dx d) [ (4 - x2) dx 0 2Find the particular solution of the equation f'(x) = 2x2 that satisfies the condition f(1) = 6. a) f(x) = 4Vx + 2 b) f (x ) = 4x + C c) f(x) = V2x + 6 - 2 V2 d) f(x) = 2vx + 4Using the table of values shown above for the continuous function h(x), which of the 9 following is the approximation of I h(x)dx using 4 trapezoids with equal subintervals? 1 a)27 b)26 c)24 d)22 Use the properties of integrals to evaluate the following integral, given that: (f(x) dx = 10 and (f ( x) dx = 3 0 S5 f (z)Use the properties of integrals to evaluate the following integral, given that: [f(x) dix = 10 and [f ( x) dx = 3 0 5 So f (z) =f ( x ) -8-7-6-5-4-3-2-1 0 1 2 3 4 5 6 78 9 Using the graph of f(x) shown above, what is the value of f(x) dx ? -7 Saf (x) da