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Sujay
Solve the following Definite Integral purely analytically (no graphs or calculators):
\[\int\limits_{0}^{5}∣(x^2−5x+4)∣dx\]
You have to split this one up into three different integrals:|dw:1360284094229:dw| You have to flip that dip below the x-axis across the x-axis (it's absolute valut is positive. The integrate 0 to 1, (-1) times 1 to 4 , and then 4 to 5. Add em up.
This is three separate integrals: x^3/3, -5x^2/2, and 4x. Evaluate each of these from 0 to 5: (5^3/3 - 5*5^2/2 +4(5)) - (0^3/3 - 5*0^2/2 +4(0). The second part all goes to zero, so you're left with 125/3 - 125/2 +20. Over a common denominator that is (250-375+120)/6, = (370 - 375)/6 = -5/6. Your answer is -5/6.