5 4 什 Y f(x) 3 6 9 f(x)=√ 6x-x² g(x)=4-|x-10| h(x)=1 |x-15| g(x) 12 h(x) 15 + x Use the formulas for areas of triangles and semicircles to evaluate the integrals of the functions graphed in the figure. Enter the sum of all shaded areas in terms of л.
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- f(x)= square root of 4x -x2 g(x)=square root of -48+16x-x2 h(x)=1-|x-13| Evaluate the integrals of the functions graphed using the formulas for areas of triangles and circles. Enter the sum of all shaded areas in terms of π.The curves f(x)= 3-x^2 and g(x) =e^(2x)-1 are shown in the figure. Let R be the shaded region bounded by the graph of f (x), g(x) and the y-axis. The vertical line x=k divides R into two regions where the area of the region to the left of the line x=k is (2/3) the area of the region to the right of the line. Write, but do not solve, an equation involving integral expressions whose solution gives the value of k.g(x) = 2x2 − x − 1, [3, 5], 4 rectangles Use left and right endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval.
- The graph of ƒ(x) = 6x(x + 1)(x - 2) is shown . The region R1 is bounded by the curve and the x-axis on theinterval [-1, 0], and R2 is bounded by the curve and the x-axis on the interval [0, 2].a. Find the net area of the region between the curve and the x-axis on [-1, 2].b. Find the area of the region between the curve and the x-axis on [-1, 2].Evaluate the integrals of the functions graphed using the formulas for areas of triangles and semicircles. Enter the sum of all shaded areas in terms of π.Shaded areasf(x)= square root of 8x-x^2g(x)=2-|x-10|h(x)=1-|x-13|The curves f(x) = 3-x^2 and g(x) = e^2x-1 are shown in the figure. Let R be the shaded region bounded by the graph if f(x), g(x) and the y axis. The vertical line x=k divides R into two regions where the area of the region to the left of the line x=k is 2/3 the area of the region to the right of the line. Write, but do not solve, an equation involving integral expressions whose solution gives the value of k.
- Use right and left endpoints and the given number of rectangles to find two approximations of the area of the region between the graph of the function and the x-axis over the given interval. f(x) = 2x + 6, [0, 2], 4 rectangles there is one part of the problem I do not know how to fill out. its picture is on a separate attachment if you fill out the rest of these problem, I should be able to do the other half of the problem on my own.# 10) Solve this application of improper integral problem. Show your complete answer with a graph in a given-required-solution without the use of calculator.A piece of cardboard measuring 12 inches by 9 inches is formed into an open-top box by cutting squares with side length xx from each corner and folding up the sides.Find a formula for the volume of the box in terms of xxV(x) = Find the value for xx that will maximize the volume of the box (round your answer to the nearest hundredth place).x =
- 6. 1. Evaluate the definite integral. Show your complete solution.How does the method of substitution work for definite integrals? Give examples.Use the method of partial fractions to evaluate the integral. (Hint: Use the rational root theorem. Use C for the constant of integration. Remember to use absolute values where appropriate.) 3x + 4 x3 − 2x − 4 dx