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Chapter - Integrals

Topic – Definite integrals

Subtopic – Properties of definite integrals P3,P4(PART-B)

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PROPERTIES OF DEFINITE INTEGRALS�

Properties P3, P4

(PART-B)

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PROPERTY-P3

  • If f(x) is continuous on [a,b] then

​

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PROPERTY-3

PROOF:

Let I =

Put t= a + b - x

dt = - dx.

When x=a then t= b ; When x=b, then t= a.

=

=

( By prop p1 )

dt

dt

dx

=

( By prop P0 )

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PROPERTY-P4

  • If f(x) is continous on [0,a] then

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PROOF

  • We know that

​

Apply this formula to

​

= dx

​

=

​

dx

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