Question
Download Solution PDFFind the area between the curve y = x2 and y = x.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
The area between the curves y1 = f(x) and y2 = g(x) is given by:
Area enclosed =
Where, x1 and x2 are the intersections of curves y1 and y2
Calculation:
Given
Curve 1: y = x2 = f(x) (say)
Curve 2: y - x = 0
⇒ y = 8 - 6x = g(x) (say)
To find the intersections (or limits of the area) putting value of y from curve 1
⇒ x2 - x = 0
⇒ x(x - 1) = 0
⇒ x = 0, x = 1
Now the required area (A) is
A =
⇒ A =
⇒ A =
⇒ A =
⇒ A =
Additional Information
Integral property:
- ∫ xn dx =
+ C ; n ≠ -1 + C - ∫ ex dx = ex+ C
- ∫ ax dx = (ax/ln a) + C ; a > 0, a ≠ 1
- ∫ sin x dx = - cos x + C
- ∫ cos x dx = sin x + C
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