4 For the function v=12sin 40 , calculate the integral. What is the specific value of the area over a range of Osos" radians. 5 A complex function can be modelled by the equation: S (3x? ) ( x ) + 7) dx Find the indefinite integral of the function using the substitution u = x +7 6 The acceleration of an object moving in a strange way has been modelled as a=ex . a) Use integration by parts to find an equation to model the velocity v if v= fe*xdx . b) Is the problem any different if you find v= [ xe" dx ? 7 Newton's law states F = ma. Find the integral of F when m can be modelled by e-7 and a can be modelled by 5t? between the limits of 3 and 1 . Checklist of evidence Your informal report should contain: required analysis worked solutions to the problems Each worked solution should be laid out clearly and contain brief explanations of the stages of the calculation to indicate your understanding of how calculus can be used to solve an engineering problem. Graphs should be well presented and clearly labelled and comparisons between methods should be accurate and well presented. Criteria covered by this task: Unit/Criteria reference To achieve the criteria you must show that you are able to: Evaluate, using technically correct language and a logical structure, the 7/B.D1 correct integral calculus and numerical integration solutions for each type of given routine and non-routine functions, including at least two set in an engineering context. Find accurately the integral calculus and numerical integration 7/B.M2 solutions for each type of given routine and non-routine function, and find the properties of periodic functions. 7/B.P4 Find the indefinite integral for each type of given routine function. 7/B.P5 Find the numerical value of the definite integral for each type of given routine function. 7/B.P6 Find, using numerical integration and integral calculus, the area under