Maths : Applications of Integration: Summary

**SUMMARY**

(i) The
area of the region bounded by a curve, above *x* -axis and the lines *x* =
*a* and *x* = *b *is A = ^{b}âˆ«_{a}
*y dx* .

(ii) The
area of the region bounded by a curve, below*
x *-axis and the lines* x *= a and* x *=*
b *is A = âˆ’^{b}âˆ«_{a} *ydx*
= | ^{b}âˆ«_{a} *ydx* | .

(iii) Thus
area of the region bounded by the curve to the right of* y *-axis, the lines* y *= c
and *y* = *d* is *A* = ^{d}âˆ«_{c}
*xdy
.*

(iv) The
area of the region bounded by the curve to the left of* y *-axis, the lines* y *= c
and *y* = *d* is A = âˆ’ ^{d}âˆ«_{c}* x*dy = **|** ^{d}âˆ«_{c}
x*dy |.*

(v) If *fâ€‰(x) â‰¥ g(x*), then area bounded by the
curves and the lines* x *= *a*,*
x *=* b *is

A = ^{b}âˆ«_{a}
[ *f (x)* âˆ’ g( x)]*dx* = ^{b}âˆ«_{a} ( y_{U} âˆ’ y_{L} ) *dx*

(vi) If *f*â€‰(*y*)
â‰¥ *g*(*y*), then area bounded by the curves and the lines* y *= *c*,* y *= *d
*is

A = ^{d}âˆ«_{c}
[* f *( *y*) âˆ’ *g*(*y*)]*dy*
= ^{d}âˆ«_{c} ( x_{R} âˆ’ x_{L} )* dy*

(i) The
volume of the solid of revolution about *x-*axis
is *V* = *Ï€ *^{b}âˆ«_{a}* **y*^{2}* **dx*.

(ii) The
volume of the solid of revolution about *y-*axis
is *V* = *Ï€*^{
d}âˆ«_{c}* x*^{2}* **dy*.

Tags : Applications of Integration | Mathematics , 12th Maths : UNIT 9 : Applications of Integration

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12th Maths : UNIT 9 : Applications of Integration : Summary | Applications of Integration | Mathematics

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