13.2 a) integrate (3x) dx from 0 to 3 Plot[3x,Piecewise[{{0, 0<=x<=1}, {3, 2>x>1}, {6, 3>x>2}}], {x, 0, 3}] Plot[3x,Piecewise[{{3, 0<=x<=1}, {6, 2>x>1}, {9, 3>x>2}}], {x, 0, 3}] Plot[3x,Piecewise[{{1.5, 0<=x<=1}, {4.5, 2>x>1}, {7.5, 3>x>2}}], {x, 0, 3}] c) integrate (4x-x^2) dx from 1 to 4 Plot[4x-x^2,Piecewise[{{4*1.0-1.0^2, 1.5>x>1}, {4*1.5-1.5^2, 2>x>1.5}, {4*2.0-2.0^2, 2.5>x>2}, {4*2.5-2.5^2, 3>x>2.5}, {4*3.0-3.0^2, 3.5>x>3}, {4*3.5-3.5^2, 4>x>3.5}}], {x, 1, 4}] Plot[4x-x^2,Piecewise[{{4*1.5-1.5^2, 1.5>x>1}, {4*2.0-2.0^2, 2>x>1.5}, {4*2.5-2.5^2, 2.5>x>2}, {4*3.0-3.0^2, 3>x>2.5}, {4*3.5-3.5^2, 3.5>x>3}, {4*4.0-4.0^2, 4>x>3.5}}], {x, 1, 4}] Plot[4x-x^2,Piecewise[{{4*1.25-1.25^2, 1.5>x>1}, {4*1.75-1.75^2, 2>x>1.5}, {4*2.25-2.25^2, 2.5>x>2}, {4*2.75-2.75^2, 3>x>2.5}, {4*3.25-3.25^2, 3.5>x>3}, {4*3.75-3.75^2, 4>x>3.5}}], {x, 1, 4}] d) integrate sqrt(x) dx from 1 to 4 Plot[sqrt(x), Piecewise[{{sqrt(1), 2.0>x>1.00}, {sqrt(2), 3.0>x>2.00}, {sqrt(3), 4.0>x>3.00}}], {x, 1, 4}] Plot[sqrt(x), Piecewise[{{sqrt(2), 2.0>x>1.00}, {sqrt(3), 3.0>x>2.00}, {sqrt(4), 4.0>x>3.00}}], {x, 1, 4}] Plot[sqrt(x), Piecewise[{{sqrt(1.5), 2.0>x>1.00}, {sqrt(2.5), 3.0>x>2.00}, {sqrt(3.5), 4.0>x>3.00}}], {x, 1, 4}] 13.3 a) plot x^2, 2-x integrate 2-x-x^2 dx from -2 to 1 b) plot sqrt(4-x^2) where x from -2 to 2 integrate sqrt(4-x^2) dx from -2 to 2 c) plot x^2,x^3 where x from -0.25 to 1.25 integrate x^2-x^3 dx from 0 to 1 d) plot x^2/4,x,1 where x from -2 to 1 integrate x-x^2/4 dx from 0 to 1 f) plot x^3/3-x, x/3 integrate |x/3-(x^3/3-x)| dx from -2 to 2 13.4 a) integrate (x/2+3) dx from -2 to 4 b) integrate sqrt(9-x^2) dx from -3 to 3 c) integrate 1-|x| dx from -1 to 1 d) integrate (1+sqrt(1-x^2)) dx from -1 to 1 13.5 plot x^3,(x-1)^3 where x from 0 to 2 13.7 plot x-x^2 13.8 a) integrate 2x^2+1 dx from -3 to 2 b) integrate (x+5)/(x^2) dx from -5 to -1 d) integrate sin^2(x/2) dx from -pi/2 to pi/2 e) integrate (3x^4+6x^2+1)/(x^2+1)dx from -1 to 1 f) integrate ((sin (2x))^3)/((cos x)^3) from -pi/3 to pi/3