21- Iff(x) =J3 (1 - t ; 6'2"dz 22' Iffoc) = osmx V1 + t2 dt and g(}') = Eflx) dx, find 9"(7T/6) 23- On what interval is the curve 2 I I O ' 2)6' dt, on what interval 18 f mcreasmg? mdx y = J'x t2 dt 0 t2 + t + 2 concave downward? 24. Find the slope of the tangent line to the curve with parametric equations x =w/1 + u3 du, y = 1 + 2t - t3 at the point (0, 1). ' 25- Ifffl) = 12, f' is continuous, and fff'bc) dx = 17, what is the value of f(4)? ' 26. T ' I + r3 dr he error function - 2 x -,2 * erf(x)-- fifo e dt is used in probability, statistics, and engineering. (a) Show that fj e-'2 dt = HF [erf(b) - erf(a)]. (b) Show that the function y = exzerf(x) satisfies the differ- ential equation y' = 2xy + 2/fi. 27. The Fresnel function S was defined in Example 4 and graphed in Figures 6 and 7. (a) At what values of x does this function have local maximum values? (b) On what intervals is the function concave upward? [mph (c) Use a graph to solve the following equation correct to two ' decimal places:21- Iff(x) =J3 (1 - t ; 6'2"dz 22' Iffoc) = osmx V1 + t2 dt and g(}') = Eflx) dx, find 9"(7T/6) 23- On what interval is the curve 2 I I O ' 2)6' dt, on what interval 18 f mcreasmg? mdx y = J'x t2 dt 0 t2 + t + 2 concave downward? 24. Find the slope of the tangent line to the curve with parametric equations x =w/1 + u3 du, y = 1 + 2t - t3 at the point (0, 1). ' 25- Ifffl) = 12, f' is continuous, and fff'bc) dx = 17, what is the value of f(4)? ' 26. T ' I + r3 dr he error function - 2 x -,2 * erf(x)-- fifo e dt is used in probability, statistics, and engineering. (a) Show that fj e-'2 dt = HF [erf(b) - erf(a)]. (b) Show that the function y = exzerf(x) satisfies the differ- ential equation y' = 2xy + 2/fi. 27. The Fresnel function S was defined in Example 4 and graphed in Figures 6 and 7. (a) At what values of x does this function have local maximum values? (b) On what intervals is the function concave upward? [mph (c) Use a graph to solve the following equation correct to two ' decimal places