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Integrals - Class 12 Engineering Maths - Extra Questions

The value  of the definite integral, I=100xex2dx is equal to 



2π0cos5xdx



Write the value of 1sinxcos2xdx



22π01sinxdx=



Prove that:
π0xdx1+sinx=π



Evaluate the following definite integral:

124x dx



Evaluate the following definite integral:
π/20sinxcosx dx 



Evaluate the following definate integral:
203x+2 dx



10dx(1+x)(2+xx2)=1k2. Find the value of k.



Integrate 10sin1(2x1+x2)dx



Evaluate: 10x4(1x)41+x2dx



10cot1(1+x2x)dx.



Prove that tanx1/et1+t2dt+cotx1/e1t(1+t2)dt=1.



Evaluate:
π/40sinx+cosx9+16sin2xdx



Evaluate:
0214x2dx



EVALUATE 
321x+5dx



Evaluate the definite integral:
101x2(1+x2)2dx



Evaluate: 12x+3dx



Evaluate the following integrals:
2x2+3x+4dx



Evaluate the following integral:
(x+1)2x2+3dx



Evaluate the following integrals:
2axx2dx



Evaluate the following definite integral:

π/40sin32tcos2t dt.



Evaluate the following integral:
20x2xdx.



Evaluate the following integral:
90dx(1+x).



Evaluate the following integral:
32(2x)5x6x2dx.



Evaluate the following integral:
a0xa2+x2dx.



Evaluate the following integral:
21dx(x+1)x21.



Evaluate the following integral:
10x31+3x4dx.



Evaluate the following integral:
a0x4a2x2dx.



Evaluate the following integral:
10(1x2)(1+x2)2dx.



Prove that 41x(5x+x)dx=32.



Prove that 10x(1x)5dx=142.



Prove that 0x(1+x)(1+x2)dx=π4.



Prove that 3a/4a/4x(ax+x)dx=a4.



Prove that 80|x5|dx=17.



Prove that a0x(x+ax)dx=a2.



Prove that a0dxx+a2x2=π4.



Prove that 20x2xdx=16215.



Prove that 22|x+1|dx=5.



The value of the integral 99990dx(x+1+x2)100 is



Let I=10dx4x2x3 and I1=1/20dx1x4



Find : π20dx4+5cosxdx



π/40(sinx+cosx)9+16sin2xdx



21x2x2+1dx



Evaluate: 31dx1+x2



Evaluate: π20sinxcosx1+sin4xdx.



If the value of the definite integral2070C7x200(1x)7dx is equal to 1k where kN, thenthe value of k/26 is



Class 12 Engineering Maths Extra Questions