Evaluate int_{-3}^{1} e^{3 x}+9 x^{2}-8 d x

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Accepted Answer

Step:1 ：Evaluate (int_{-3}^{1} e^{3 x}+9 x^{2}-8 d x)Step:2 ：Integrate each term separately: (int e^{3x} dx = frac{1}{3}e^{3x}), (int 9x^2 dx = 3x^3), (int -8 dx = -8x)Step:3 ：Evaluate the resulting expression from -3 to 1: (left[frac{1}{3}e^{3x} + 3x^3 - 8xright]_{-3}^{1})Step:4 ：Substitute the limits of integration: (left[frac{1}{3}e^{3(1)} + 3(1)^3 - 8(1)right] - left[frac{1}{3}e^{3(-3)} + 3(-3)^3 - 8(-3)right])Step:5 ：Simplify the expression: (-frac{1}{3}e^{-9} + frac{1}{3}e^{3} + 52)Step:6 ：Calculate the final result: (58.6951378377945)Step:7 ：Final Answer: (boxed{58.695})

Answer

Step: 1 ：Evaluate (int_{-3}^{1} e^{3 x}+9 x^{2}-8 d x)Step: 2 ：Integrate each term separately: (int e^{3x} dx = frac{1}{3}e^{3x}), (int 9x^2 dx = 3x^3), (int -8 dx = -8x)Step: 3 ：Evaluate the resulting expression from -3 to 1: (left[frac{1}{3}e^{3x} + 3x^3 - 8xright]_{-3}^{1})Step: 4 ：Substitute the limits of integration: (left[frac{1}{3}e^{3(1)} + 3(1)^3 - 8(1)right] - left[frac{1}{3}e^{3(-3)} + 3(-3)^3 - 8(-3)right])Step: 5 ：Simplify the expression: (-frac{1}{3}e^{-9} + frac{1}{3}e^{3} + 52)Step: 6 ：Calculate the final result: (58.6951378377945)Step: 7 ：Final Answer: (boxed{58.695})

Evaluate $\int_{- 3}^{1} e^{3 x} + 9 x^{2} - 8 d x$

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Evaluate $\int_{- 3}^{1} e^{3 x} + 9 x^{2} - 8 d x$