Question

Question 1 :
The area between two curves y=f(x) and
y=g(x) having two point of intersection at
x=a and x=b is equal to
So [f(*) – g()] d
So [f(x)9(x)] da
f (x) dx so gx
(x) dx
S' [f(x) +g(*)] da
cb
b
☺​

Answer 1

The correct answer is $\int\limits^b_a {|f(x)-g(x)|} \, dx$.

Given: Graphs: y=f(x) and y=g(x)

Points of intersection = x=a and x=b

To Find: Area between two curves.

Solution:

If f(x) > g(x)

Area = $\int\limits^b_a {f(x)-g(x)} \, dx$

If g(x) > f(x)

Area = $\int\limits^b_a {g(x)-f(x)} \, dx$

We can conclude that area will be = $\int\limits^b_a {|f(x)-g(x)|} \, dx$.

Hence, the answer is  $\int\limits^b_a {|f(x)-g(x)|} \, dx$.

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