Bài 2: Tích phân
Các câu hỏi tương tự
1, I intlimits^1_0dfrac{2x+1}{x^2+x+1}dx
2,intlimits^{dfrac{1}{2}}_0dfrac{5xdx}{left(1-x^2right)^3}
3, intlimits^1_0dfrac{2x}{left(x+1right)^3}dx
4, intlimits^1_0dfrac{4x-2}{left(x^2+1right)left(x+2right)}dx
5, intlimits^1_0dfrac{x^2dx}{x^6-9}
6, intlimits^2_1dfrac{2x-1}{x^2left(x+1right)}dx
Đọc tiếp
1, I = \(\int\limits^1_0\dfrac{2x+1}{x^2+x+1}dx\)
2,\(\int\limits^{\dfrac{1}{2}}_0\dfrac{5xdx}{\left(1-x^2\right)^3}\)
3, \(\int\limits^1_0\dfrac{2x}{\left(x+1\right)^3}dx\)
4, \(\int\limits^1_0\dfrac{4x-2}{\left(x^2+1\right)\left(x+2\right)}dx\)
5, \(\int\limits^1_0\dfrac{x^2dx}{x^6-9}\)
6, \(\int\limits^2_1\dfrac{2x-1}{x^2\left(x+1\right)}dx\)
Tính các tích phân sau :
a) intlimits^1_0left(y^3+3y^2-2right)dy
b) intlimits^4_1left(t+dfrac{1}{sqrt{t}}-dfrac{1}{t^2}right)dt
c) intlimits^{dfrac{pi}{2}}_0left(2cos x-sin2xright)dx
d) intlimits^1_0left(3^s-2^sright)^2ds
e) intlimits^{dfrac{pi}{3}}_0cos3xdx+intlimits^{dfrac{3pi}{2}}_0cos3xdx+intlimits^{dfrac{5pi}{2}}_{dfrac{3pi}{2}}cos3xdx
g) intlimits^3_0left|x^2-x-2right|dx
h) intlimits^{dfrac{5pi}{4}}_{pi}dfrac{sin x-cos x}{sqrt{1+sin2x}}dx
i) intlimits^4_0dfrac{4x-1}{sqrt{2x+1}+2}dx
Đọc tiếp
Tính các tích phân sau :
a) \(\int\limits^1_0\left(y^3+3y^2-2\right)dy\)
b) \(\int\limits^4_1\left(t+\dfrac{1}{\sqrt{t}}-\dfrac{1}{t^2}\right)dt\)
c) \(\int\limits^{\dfrac{\pi}{2}}_0\left(2\cos x-\sin2x\right)dx\)
d) \(\int\limits^1_0\left(3^s-2^s\right)^2ds\)
e) \(\int\limits^{\dfrac{\pi}{3}}_0\cos3xdx+\int\limits^{\dfrac{3\pi}{2}}_0\cos3xdx+\int\limits^{\dfrac{5\pi}{2}}_{\dfrac{3\pi}{2}}\cos3xdx\)
g) \(\int\limits^3_0\left|x^2-x-2\right|dx\)
h) \(\int\limits^{\dfrac{5\pi}{4}}_{\pi}\dfrac{\sin x-\cos x}{\sqrt{1+\sin2x}}dx\)
i) \(\int\limits^4_0\dfrac{4x-1}{\sqrt{2x+1}+2}dx\)
Áp dụng phương pháp tính tích phân, hãy tính các tích phân sau :
a) intlimits^{dfrac{pi}{2}}_0xcos2xdx
b) intlimits^{ln2}_0xe^{-2x}dx
c) intlimits^1_0lnleft(2x+1right)dx
d) intlimits^3_2left|lnleft(x-1right)-lnleft(x+1right)right|dx
e) intlimits^2_{dfrac{1}{2}}left(1+x-dfrac{1}{x}right)e^{x+dfrac{1}{x}}dx
g) intlimits^{dfrac{pi}{2}}_0xcos xsin^2xdx
h) intlimits^1_0dfrac{xe^x}{left(1+xright)^2}dx
i) intlimits^e_1dfrac{1+xln x}{x}e^xdx
Đọc tiếp
Áp dụng phương pháp tính tích phân, hãy tính các tích phân sau :
a) \(\int\limits^{\dfrac{\pi}{2}}_0x\cos2xdx\)
b) \(\int\limits^{\ln2}_0xe^{-2x}dx\)
c) \(\int\limits^1_0\ln\left(2x+1\right)dx\)
d) \(\int\limits^3_2\left|\ln\left(x-1\right)-\ln\left(x+1\right)\right|dx\)
e) \(\int\limits^2_{\dfrac{1}{2}}\left(1+x-\dfrac{1}{x}\right)e^{x+\dfrac{1}{x}}dx\)
g) \(\int\limits^{\dfrac{\pi}{2}}_0x\cos x\sin^2xdx\)
h) \(\int\limits^1_0\dfrac{xe^x}{\left(1+x\right)^2}dx\)
i) \(\int\limits^e_1\dfrac{1+x\ln x}{x}e^xdx\)
Tính các tích phân sau đây :
a) intlimits^{dfrac{pi}{2}}_0left(x+1right)cosleft(x+dfrac{pi}{2}right)dx
b) intlimits^1_0dfrac{x^2+x+1}{x+1}log_2left(x+1right)dx
c) intlimits^1_{dfrac{1}{2}}dfrac{x^2-1}{x^4+1}dx (đặt tx+dfrac{1}{x} )
d) intlimits^{dfrac{pi}{2}}_0dfrac{sin3xdx}{3+4sin x-cos2x}dx
Đọc tiếp
Tính các tích phân sau đây :
a) \(\int\limits^{\dfrac{\pi}{2}}_0\left(x+1\right)\cos\left(x+\dfrac{\pi}{2}\right)dx\)
b) \(\int\limits^1_0\dfrac{x^2+x+1}{x+1}\log_2\left(x+1\right)dx\)
c) \(\int\limits^1_{\dfrac{1}{2}}\dfrac{x^2-1}{x^4+1}dx\) (đặt \(t=x+\dfrac{1}{x}\) )
d) \(\int\limits^{\dfrac{\pi}{2}}_0\dfrac{\sin3xdx}{3+4\sin x-\cos2x}dx\)
chứng minh:
\(\int\limits^1_0\dfrac{ln\left(x+\sqrt{1-x^2}\right)}{x}dx=\dfrac{3}{4}\int\limits\dfrac{ln\left(1+x\right)}{x}^1_0dx\)
Tính các tích phân sau :
a) intlimits^{dfrac{1}{2}}_{-dfrac{1}{2}}sqrt[3]{left(1-xright)^2dx}
b) intlimits^{dfrac{pi}{2}}_0sinleft(dfrac{pi}{4}-xright)dx
c) intlimits^2_{dfrac{1}{2}}dfrac{1}{xleft(x+1right)}dx
d) intlimits^2_0xleft(x+1right)^2dx
e) intlimits^2_{dfrac{1}{2}}dfrac{1-3x}{left(x+1right)^2}dx
g) intlimits^{dfrac{pi}{2}}_{-dfrac{pi}{2}}sin3xcos5xdx
Đọc tiếp
Tính các tích phân sau :
a) \(\int\limits^{\dfrac{1}{2}}_{-\dfrac{1}{2}}\sqrt[3]{\left(1-x\right)^2dx}\)
b) \(\int\limits^{\dfrac{\pi}{2}}_0\sin\left(\dfrac{\pi}{4}-x\right)dx\)
c) \(\int\limits^2_{\dfrac{1}{2}}\dfrac{1}{x\left(x+1\right)}dx\)
d) \(\int\limits^2_0x\left(x+1\right)^2dx\)
e) \(\int\limits^2_{\dfrac{1}{2}}\dfrac{1-3x}{\left(x+1\right)^2}dx\)
g) \(\int\limits^{\dfrac{\pi}{2}}_{-\dfrac{\pi}{2}}\sin3x\cos5xdx\)
Hãy chỉ ra kết quả nào dưới đây đúng :
a) intlimits^{dfrac{pi}{2}}_0sin xdx+intlimits^{dfrac{3pi}{2}}_{dfrac{pi}{2}}sin xdx+intlimits^{2pi}_{dfrac{3pi}{2}}sin xdx0
b) intlimits^{dfrac{pi}{2}}_0left(sqrt[3]{sin x}-sqrt[3]{cos x}right)dx0
c) intlimits^{dfrac{1}{2}}_{-dfrac{1}{2}}lndfrac{1-x}{1+x}dx0
d) intlimits^2_0left(dfrac{1}{1+x+x^2+x^3}+1right)dx0
Đọc tiếp
Hãy chỉ ra kết quả nào dưới đây đúng :
a) \(\int\limits^{\dfrac{\pi}{2}}_0\sin xdx+\int\limits^{\dfrac{3\pi}{2}}_{\dfrac{\pi}{2}}\sin xdx+\int\limits^{2\pi}_{\dfrac{3\pi}{2}}\sin xdx=0\)
b) \(\int\limits^{\dfrac{\pi}{2}}_0\left(\sqrt[3]{\sin x}-\sqrt[3]{\cos x}\right)dx=0\)
c) \(\int\limits^{\dfrac{1}{2}}_{-\dfrac{1}{2}}\ln\dfrac{1-x}{1+x}dx=0\)
d) \(\int\limits^2_0\left(\dfrac{1}{1+x+x^2+x^3}+1\right)dx=0\)
Tính các tích phân sau
1.Iintlimits^{frac{Pi}{4}}_0 (x+1)sin2xdx
2.Iintlimits^2_1frac{x^2+3x+1}{x^2+x}dx
3.Iintlimits^2_1frac{x^2-1}{x^2}lnxdx
4. Iintlimits^1_0xsqrt{2-x^2}dx
5.Iintlimits^1_0frac{left(x+1right)^2}{x^2+1}dx
6. Iintlimits^5_1frac{dx}{1+sqrt{2x-1}}
7. Iintlimits^3_1frac{1+lnleft(x+1right)}{x^2}dx
8.Iintlimits^1_0frac{x^3}{x^4+3x^2+2}dx
9. Iintlimits^{frac{Pi}{4}}_0xleft(1+sin2xright)dx
10. Iintlimits^3_0frac{x}{sqrt{x+1}}dx
Đọc tiếp
Tính các tích phân sau
1.I=\(\int\limits^{\frac{\Pi}{4}}_0\) (x+1)sin2xdx
2.I=\(\int\limits^2_1\frac{x^2+3x+1}{x^2+x}dx\)
3.I=\(\int\limits^2_1\frac{x^2-1}{x^2}lnxdx\)
4. I=\(\int\limits^1_0x\sqrt{2-x^2}dx\)
5.I=\(\int\limits^1_0\frac{\left(x+1\right)^2}{x^2+1}dx\)
6. I=\(\int\limits^5_1\frac{dx}{1+\sqrt{2x-1}}\)
7. I=\(\int\limits^3_1\frac{1+ln\left(x+1\right)}{x^2}dx\)
8.I=\(\int\limits^1_0\frac{x^3}{x^4+3x^2+2}dx\)
9. I=\(\int\limits^{\frac{\Pi}{4}}_0x\left(1+sin2x\right)dx\)
10. I=\(\int\limits^3_0\frac{x}{\sqrt{x+1}}dx\)
Sử dụng phương pháp tính tích phân từng phần, hãy tính :
a) \(\int\limits^{\dfrac{\pi}{2}}_0\left(x+1\right)\sin x.dx\)
b) \(\int\limits^e_1x^2lnxdx\)
c) \(\int\limits^1_0ln\left(1+x\right)dx\)
d) \(\int\limits^1_0\left(x^2-2x-1\right)e^{-x}dx\)