Answer to Question #131760 in Calculus for Navya Sharma

Question #131760
evaluate limit 6 to 0 ∫ f(x)dx if f(x){x^2,x<2,3x-2,x>=2}
1
Expert's answer
2020-09-08T16:33:58-0400

"\\int \\limits_0^6 f(x)\\,dx=\\int \\limits_0^2 x^2\\,dx+\\int \\limits_2^6 (3x-2)\\,dx=\\\\=\\frac{x^3}3 \\bigg|_0^2 +3\\frac{x^2}2 \\bigg|_2^6 - 2x \\bigg|_2^6 =\\\\= \\frac{8}3+\\frac{3}2 (36-4) - 2 (6-2) = 42\\frac{2}3\\\\\n\\int\\limits_6^0 f(x)\\,dx=-\\int\\limits_0^6f(x)\\,dx=>\\int\\limits_6^0 f(x)\\,dx=-42\\frac{2}3"


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