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ACCURATE PUBLICATION-DEFINITE INTEGRALS-QUESTION CARRYING 1 MARK - TYPE-III
- int(a)^(b)f(x)dx represents the area of the region bounded by the curv...
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- Let f be a continuous function on the closed interval [a, b] and let A...
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- int(a)^(b)f(x)dx=F(b)-F(a).
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- int(a)^(b)f(x)dx=int(a)^(b)f(z)dz.
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- int(a)^(b)f(x)dx=int(b)^(a)f(x)dx.
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- int(a)^(b)f(x)dx=int(a)^(c)f(x)dx+int(c)^(b)f(x)dx.
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- int(0)^(a)f(x)dx=int(a)^(0)f(a-x)dx.
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- int(0)^(2a)f(x)dx=int(0)^(a)f(x)dx+int(0)^(a)f(2a-x)dx.
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- If f(x) is an odd function, then int(-a)^(a)f(x)dx=0.
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- Evaluate int(0)^(pi/4)(sin2x)dx
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- int(0)^(1)(2x)/(1+x^(2))dx=log2
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- int(0)^(1)(2x)/(5x^(2)+1)dx=log6
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- If int(0)^(1)(3x^(2)+2x+k)dx=0, then k = -2.
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- If f(x)=int(0)^(x)tsintdt, then f'(x)=xsinx.
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- If f(x) is an odd function, then int(-a)^(a)f(x)dx=0.
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- int(a)^(b)f(x)dx=int(a)^(b)f(a+b-x)dx.
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- int(-pi/4)^(pi/4)sin^(3)xdx=2.
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- int(0)^(pi/2)logtanxdx=0.
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- Evaluate : int(e)^(e^(2))(dx)/(xlogx)
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