三、解答题-|||-1.计算 (int )_(1)^3((x)^3+dfrac (3)(x)+1)dx-|||-2.计算 (int )_(0)^2pi |sin t|dt-|||-3.计算 (int )_(0)^dfrac (pi {2)}sin x(cos )^5xdx.-|||-4.计算 (int )_(0)^1dfrac (sqrt {x)}(1+sqrt {x)}dx-|||-5.计算 (int )_(0)^1(x)^2(e)^xdx-|||-6.计算 (int )_(0)^+infty dfrac (arctan x)({(1+{x)^2)}^dfrac (3{2)}}dx-|||-7.求由 =(2)^x 与直线 y=1-x =1 所围成平面图形的面积.-|||-8.求由抛物线 ^2=4x 与直线 x=1 所围成图形绕x轴旋转所得的旋转体体-|||-积.

1.计算下列定积分:-|||-(1) (int )_(dfrac {pi )(3)}^pi sin (x+dfrac (pi )(3))dx-|||-(2) (

1.计算下列定积分:-|||-(1) (int )_(dfrac {pi )(3)}^pi sin (x+dfrac (pi )(3))dx ;-|||-(2)

2.计算下列定积分:-|||-(1) (int )_(dfrac {pi )(3)}^pi sin (x+dfrac (pi )(3))dx;-|||-(2)

计算(int )_(-2)^1dfrac (1)({(7+3x))^3}dx-|||-__时，令(int )_(-2)^1dfrac (1)({(7+3x))^

1.计算下列定积分:-|||-(1) (int )_(dfrac {pi )(3)}^pi sin (x+dfrac (pi )(3))dx ;

计算int dfrac (1)({(1-{x)^2)}^dfrac (3{2)}}dx；计算；

(int )_(-dfrac {pi )(2)}^dfrac (pi {2)}dfrac (|x|sin x)(1+{cos )^3x}dx=(int )_(-

9.计算下列积分:-|||-(1) (int )_(0)^2pi dfrac (1)(5+3sin theta )dtheta ;-|||-(2) (int

3.证明: (int )_(x)^1dfrac (dt)(1+{t)^2}=(int )_(1)^dfrac (1{x)}dfrac (dt)(1+{t)^2}

3.证明: (int )_(x)^1dfrac (dt)(1+{t)^2}=(int )_(1)^dfrac (1{x)}dfrac (dt)(1+{t)^2}