1 A car initially going 50/t/sec brakes at a constant rate (constant negative acceleration, also called deceleration), and the car comes to a stop in 5 seconds. a. Graph the velocity from t = 0 to t = 5. b. How far does the car travel? c. How far does the car travel if its initial velocity is doubled, but the car decelerates at the same constant rate?IN Verify the following integrals: S Inudu = ulnu - u + C ii. 1 dx = In| Inx] + C xinx iii. St(et ) dt = et(t - 1) + c W Integrate x7/2 + x5/2 _ x1/2 + x3/2 dx x1/2This problem will discuss the calculation and approximation of the area under the curve for y = 3x over the interval [2,7]. Make sure to always include a graph with a definite integral, indicating the quantity calculated with a shaded region. a. Calculate the actual, exact area using integral calculus and the fundamental theorem. b. Calculate a Left Riemann Sum using n = 5 rectangles. C. Calculate a Right Riemann Sum using n = 5 rectangles. d. Find the average of the Left and Right Sums.5 An Airbus A350-900 jet is ready to take off for a 15-hour nonstop flight to Singapore, the longest nonstop out of SFO! The jet needs to be traveling 275 mph to take off. If it can accelerate from 0 to 275 mph in 55 seconds, how long must the plane travel on the runway (that is, how long must the runway be)? Assume constant acceleration. Answer should include a graph. Use L'Hopital's, and a table of values and a graph to find the following limits. lim statt? ) (ii) lim xIn.xAssume that oil spilling from a ruptured tanker spreads in a circular pattern whose radius is increasing at a constant rate of two feet per second. How fast is the area of the spill increasing when the radius of the spill is at sixty feet? Given the area under the curve f(x) = on the interval [1, b]is 6. Use the Fundamental Theorem of Calculus to find b