SOLUTION :
f(x) = x^4 - 4x^3 + 12x^2 and g(x) = 5x + 22
As per given figure :
Shaded Area
0 2
= ∫ | ( g(x) - f(x) ) | dx + ∫ | ( g(x) - f(x) ) | dx
-1 0
0 2
= ∫ | ( (5x + 22) - (x^4 - 4x^3 + 12x^2) ) | dx + ∫ | ( (5x + 22) - (x^4 - 4x^3 + 12x^2) ) | dx
-1 0
0 2
= [ | 5x^2/2 + 22x - x^5 /5 + x^4 - 4x^3 | ] + [ | 5x^2/2 + 22x - x^5 /5 + x^4 - 4x^3 | ]
-1 0
= | (5(-1)^2 /2 + 22(-1) - (-1)^5/5 + (-1)^4 - 4(-1)^3 | + |( 5(2)^2 /2 +22(2) - (2)^5 /5 + (2)^4 - 4(2)^3 |
= 14.3 + 31.6
= 45.9 ( ANSWER)
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