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1.Which of the following integrals represents the area of the region bounded by x = e and thefunctions f(x) = ln(x) and g(x) = log1/e(x)? (4 points)XGraph the functions to determine the upper/lower function and the bounds for the integral.The intersection point occurs at x = 1, so that will be the lower bound with x = e as the upper.The upper function is the ln x and the lower function is log(1/e) xThe correct answer will be the first choice:e1(ln ( x ) log x)dx1e2.Which integral gives the area of the region in the first quadrant bounded by the axes, y =ex, x = ey, and the line x = 4? (4 points)XThis area will have 2 different integrals. Between x = 0 and x = 1, the graph of x = e^y (or y = lnx), will be outside of the first quadrant.The first integral will just be from 0 to 1 of the other functionThe second integral will be from x = 1 and x = 4. The upper function will be e^x and the lowerln xThe correct solution will be the second choice.3.Find the area of the region bounded by the graphs of y = 2 - x2 and y = -x. (4 points)X 4.51.5-1.833None of these2 x 2= x0= x 2 x 20= ( x 2)( x+ 1)x= 1, x= 222 x 2+ x dx1x3 x2+3 22x32 22(322 2( 1) ( 1)+ 2 ( 1)+3 23281 14 + 2 2+ +33 29 18 3 24.5())4.Find the area of the region bounded by the graphs of y = x, y = 6 - 2x, and y = 0. (4points)X 369None of theseCreate ...


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