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APPLICATION OF INTEGRALS �AREA UNDER CURVES

PRASAD NARAYANAN KANI

PGT MATHEMATICS

JNV KOLHAPUR(M.S)

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LET’S START

y = x

1

0

2

3

4

X

Y

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IGNITE YOURSELF !!

  • What is the area of triangle in the figure?

Area = ½ *base * height

= ½ * 4 * 4

=8 sq.units

Now lets us consider,

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​

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CONCEPT

  • The Area Under a curve

y = f(x) from x = a to x = b

is given by

​

X

Y

y = f(x)

x = a

x = b

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CONCEPT

X

Y

x = f(y)

y = a

y=b

The Area Under a curve

x = f(y) from y = a to y = b

is given by

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AREA BETWEEN TWO CURVES

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EXAMPLE - 1

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EXAMPLE - 2

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EXAMPLE - 3

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EXAMPLE - 3 Continuing…

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EXAMPLE - 3 Continuing…