Let f(x) = 9x^2 - 4x + 1/x - 3/x^2 + 8. Suppose that F(x) is an antiderivative o

Question

Let f(x) = 9x^2 - 4x + 1/x - 3/x^2 + 8. Suppose that F(x) is an antiderivative of f(x) such that F(1) = 22. Find F(x). A can of soda that had left in the sun is placed in a cooler of ice to cool down. After 20 minutes in the cooler. Its temperature of the soda t minutes after being placed in the cooler. Suppose that f'(t) = -2.81126e^-0.04547, What was the temperature of the soda when it was placed in the cooler? Give your result accurate to two decimal places. that F(x) is an antiderivative of f(x) such that F(1) = 22. Find F(x). A ean of soda that had been left in the sun is placed in a cooler of ice to cool down. After 20 minutes in ihe cooler, its temperature was 58 degree F. Let f(t) denote the temperature of the soda t minutes after being placed in the cooler. Suppose that f'(t) = -2.81126e^-004847. What was the temperature of the soda when it was placed in the cooler? Give your result accurate to two decimal places.

Explanation / Answer

1)f(x)=9x2 -4x +(1/x) -(3/x2)+8

F(x)= 9x2 -4x +(1/x) -(3/x2)+8 dx

F(x)= 9x2 -4x +(1/x) -3x-2+8x0 dx

xn dx =(1/(n+1))xn+1 , 1/x dx =ln(x)

F(x)=9(1/3)x3 -4(1/2)x2 +ln(x) -3(1/(-2+1))x-2+1+8x+c

F(x)=3x3 -2x2 +ln(x) +3x-1+8x+c

F(x)=3x3 -2x2 +ln(x) +(3/x)+8x+c

given F(1)=22

3 -2 +ln(1) +(3/1)+8+c=22

3-2+0+3+8+c=22

c=10

F(x)=3x3 -2x2 +ln(x) +(3/x)+8x+10

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