微积分定积分计算题求解，非常感谢 定积分题目求解！谢谢！
\u5fae\u79ef\u5206\u9898 \u5b9a\u79ef\u5206\u7684\u8ba1\u7b97\u9898 \u6c42\u5927\u795e\u7ed9\u4e2a\u8fc7\u7a0b\uff0c\u975e\u5e38\u611f\u8c22\u89e3\uff1a22\u9898\uff0c\u88ab\u79ef\u51fd\u6570ln[\u221a(1+x²)+x]\u5728\u79ef\u5206\u533a\u95f4\u4e3a\u5947\u51fd\u6570\uff0c\u2234\u6839\u636e\u5b9a\u79ef\u5206\u7684\u6027\u8d28\uff0c\u539f\u5f0f=0\u3002
23\u9898\uff0c\u88ab\u79ef\u51fd\u6570xcosx/(x²+cosx)\u5728\u79ef\u5206\u533a\u95f4\u4e3a\u5947\u51fd\u6570\uff0c\u2234\u6839\u636e\u5b9a\u79ef\u5206\u7684\u6027\u8d28\uff0c\u539f\u5f0f=0\u3002
24\u9898\uff0c\u88ab\u79ef\u51fd\u6570(xcosx²+x³)\u5728\u79ef\u5206\u533a\u95f4\u4e3a\u5947\u51fd\u6570\uff0c\u2234\u6839\u636e\u5b9a\u79ef\u5206\u7684\u6027\u8d28\uff0c\u539f\u5f0f=0\u3002
25\u9898\uff0c\u88ab\u79ef\u51fd\u6570x²tanx/(x²+1)\u5728\u79ef\u5206\u533a\u95f4\u4e3a\u5947\u51fd\u6570\uff0c\u2234\u6839\u636e\u5b9a\u79ef\u5206\u7684\u6027\u8d28\uff0c\u539f\u5f0f=0\u3002
26\u9898\uff0c\u88ab\u79ef\u51fd\u6570(tanx+sinx)\u5728\u79ef\u5206\u533a\u95f4\u4e3a\u5947\u51fd\u6570\uff0c\u2234\u6839\u636e\u5b9a\u79ef\u5206\u7684\u6027\u8d28\uff0c\u539f\u5f0f=0\u3002
27\u9898\uff0c\u539f\u5f0f=\u222be^(\u221ax)d(\u221ax)=e^(\u221ax)+C\u3002
\u4f9b\u53c2\u8003\u3002
\u5982\u56fe
=∫ x de^x
=xe^x -∫e^x dx
=xe^x -e^x +C
/
∫ x e^(-x) dx
=-∫ x de^(-x)
=-xe^(-x) +∫ e^(-x) dx
=-xe^(-x) - e^(-x) +C
/
∫(-1->1) ( |x| + e^x ) e^(-|x|) dx
=∫(-1->0) ( -x + e^x ) e^x dx +∫(0->1) ( x + e^x ) e^(-x) dx
=∫(-1->0) [ -xe^x + e^(2x) ] dx +∫(0->1) ( xe^(-x) + 1 ) dx
=[ -xe^x +e^x +(1/2)e^(2x) ]|(-1->0) +[-xe^(-x) - e^(-x) +x ]|(0->1)
={ ( 0+ 1 +1/2) -[e^(-1)+e^(-1)+(1/2)e^(-2)] }
+ [ (-e^(-1) - e^(-1) +1 ) -(0 - 1 +0 ) ]
= [ 3/2 -2e^(-1) - (1/2)e^(-2) ] + [ -2e^(-1) +2 ]
=7/2 - 4e^(-1) -(1/2)e^(-2)
绛旓細鍋滄鏃讹細v=30-1.5t-4鏍瑰彿t=0 4鏍瑰彿t+1.5t-30=0 瑙ｅ緱锛歵=100/9s dt=-1.5-2/鏍瑰彿t S=鈭玽dt=(30-1.5t-4鏍瑰彿t)*(-1.5-2/鏍瑰彿t)|(t:0-->100/9)
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绛旓細绗2棰(12棰)锛屸埖鈭(-1,1)[x^2+(x^3)sin(x^4)-鈭(1-x^2)]dx=鈭(-1,1)x^2dx+鈭(-1,1)(x^3)sin(x^4)dx-鈭(-1,1)鈭(1-x^2)dx锛岃屸埆(-1,1)x^2dx=2鈭(0,1)x^2=2/3銆佸洜(x^3)sin(x^4)鍦ㄧН鍒嗗尯闂存槸濂囧嚱鏁帮紝鏍规嵁瀹氱Н鍒鐨勬ц川锛屸埆(-1,1)(x^3)sin(x^4...
绛旓細瑙ｏ細璁緓涓轰骇閲/閿閲忋傗埖褰揅'(x)=R'(x)鏃讹紝鍒╂鼎杈惧埌鏈澶у硷紝鈭30+4x=60-2x锛寈=5銆傚張锛屾绘垚鏈嚱鏁癈(x)=鈭獵'(x)dx=鈭(30+4x)dx=30x+2x²+C锛涒埖x=0鏃剁殑鎴愭湰鏄浐瀹氭垚鏈紝鍗矯(0)=6锛屸埓C=C(0)=6銆傗埓C(x)=30x+2x²+6銆傛绘敹鐩婂嚱鏁癛(x)=鈭(0,x)R'(x)dx=...
绛旓細绉垎鏄竴绉嶈繍绠椻︹﹁F(x)涓哄嚱鏁癴(x)鐨勪竴涓師鍑芥暟锛屾垜浠妸鍑芥暟f(x)鐨勬墍鏈夊師鍑芥暟F(x)C锛圕涓轰换鎰忓父鏁帮級鍙仛鍑芥暟f(x)鐨勪笉瀹氱Н鍒(indefiniteintegral)銆傝浣溾埆f(x)dx銆備笉瀹氱Н鍒 鍏朵腑鈭彨鍋氱Н鍒嗗彿(integralsign)锛宖(x)鍙仛琚Н鍑芥暟(integrand)锛寈鍙仛绉垎鍙橀噺锛宖(x)dx鍙仛琚Н寮忥紝C鍙仛绉垎...
绛旓細浠も垰(5-x)=t锛屽垯x=5-t²锛宒x=-2tdt x=1鏃讹紝t=2锛泋=5鏃讹紝t=0锛涘師寮=鈭玔2,0]-2tdt/(1+t)=2鈭玔0,2][1 - 1/(t+1)]dt =2[t - ln(t+1)]|[0,2]=2(2-ln3)=4-2ln3
绛旓細鍒嗛儴绉垎鍗冲彲
绛旓細鈭玔1500,锛嬧垶]1000/x^2 dx =-1000(1/x)|[1500,锛嬧垶]=0-(-1000/1500)=2/3
