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For a particular object, a(t) = 4t + 7 and v(0) = 8. Find v(t). v(t) =5 Use the properties of definite integrals to find f(x) dx for the following function. 2 4x + 9 if x $ 3 f(X) = - 0.2x + 1 if x > 3 5 f ( x ) dx = 2 (Simplify your answer.)Calculate the definite integral by referring to the figure with the indicated areas. AV + A b X a a B CD Area A = 1.21 Area C = 5.798 Area B = 2.631 Area D = 1.804 . . . . . f ( x ) dx = aThe approximate rate of change in the number (in billions) of monthly text messages is given by the equation f'(t) = 7.1t 15.2 where t represents the number of years since 2000. In 2003 (t = 3) there were approximately 9.5 billion monthly text messages. Complete parts a. and b. below. a. Find the function that gives the total number (in billions) of monthly text messages in year t. f(t) = D b. According to this function, how many monthly text messages were there in 2009? D billion Find the cost function if the marginal cost function is given by C'(x) = x2! C(x) = D 5 + 6 and 32 units cost $331. Find the indefinite integral. (1 + 6 In x) 10 dx X 10 (1 + 6 In x) dx = X (Use integers or fractions for any numbers in the expression.)Use the definite integral to find the area between the x-axis and f(x) over the indicated interval. Check first to see if the graph crosses the x-axis in the given interval. f(x) = 3 ex -2; [-3,4] . . . . . The area between the x-axis and f(x) is. (Do not round until the final answer. Then round to three decimal places as needed.)Evaluate the denite integral. _ 2 _ 2 (e 2" + e 2x) (Type an integer or decimal rounded to three decimal places as needed.)