Calculus - definite integral class sheet doubts

146

Amartya Kumar Mistry ·2014-08-06 08:57:03

for the fourth q one of the roots will be zero which makes the whole integral expression zero which is independent of Î± and Î²

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Swastik Haldar thanks.
Upvote·0· Reply ·2014-08-06 09:23:30
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1357

Manish Shankar ·2014-08-06 06:03:07

First one is integral of differentiation of (xⁿ(x+a)(x+b))

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1357

Manish Shankar ·2014-08-06 06:05:40

second one is x⁸-4x⁷+6x⁶-4x⁵+x⁴1+x²

divide it to simplify it

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Swastik Haldar sir what about the sixth one? I tried diffrentiating with respect to a three times and then integrating, but it's not working.
Upvote·0· Reply ·2014-08-06 09:26:31
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Manish Shankar ·2014-08-07 06:58:49

for question 6 change the intervals to (0->pi/2)

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146

Amartya Kumar Mistry ·2014-08-07 07:28:25

for q 5 sin[Ï€/2-(Ï€/4+x)]=sin(Ï€/4+x)
now apply the rule of definite integral âˆ«_{_{^{^b}_a}}f(x)=âˆ«_{_a^{^{^b}}}f(b+a-x) and also expand sin(x+Ï€/4) by trigonometry. then after simplifying a bit you will see that numer. and denom. is getting cancelled then putting the limits you will get the result.

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146

Amartya Kumar Mistry ·2014-08-07 07:34:06

for q 8 just apply the concept of integration by parts(LIATE rule) and there for the integration of x^3/âˆš(1-x^2) take x=sinÎ¸ as substitution

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