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Express the following limit as a definite integral: lim Et ~sin (-1 + 3i n O- 2 cos( x) dx Of3 sin (x) dx OfA sin ( -2 + x) dx 2 cos ( x) dx O 2 sin (-1 + x)dxUse the limit sum definition (with right endpoints) to evaluate the following integral: A7 (x2 + 4x 8)dx v If F (x) = JA f (t) dt where f is the function whose graph is given, which of the following values is largest? y=f(t) N 4 6 8 OF(6) OF(8) OF(0) OF(2) OF(4)Consider the graph of the function g(x) given which consists of two straight lines and a semicircle. Use it to evaluate: o g (x )dx 4 y = g(x) 2 X 4 7 09 - 2T 04.5 - 2T 09 + 2 x 04. 5 + 2xEstimate the area under the graph off(x) = 9 + 2x2 from x=-1 to x=2 using six approximating rectangles and midpoints. ROUND YOUR ANSWER TO FOUR DECIMAL PLACES