# math

Let f of x equals 4 for x less than or equal to 3 and equals the quantity 7 minus x for x greater than 3. Use geometric formulas to evaluate the integral from x equals 1 to x equals 7 of f of x, dx.

I got 16 but i dont think it is right.

1. 👍 0
2. 👎 0
3. 👁 924
1. ever think of using math notation instead of words?

f(x) =
4x for x <= 3
7-x for x > 3

∫[1,7] f(x) dx
= ∫[1,3] 4x dx + ∫[3,7] 7-x dx
= 2x^2[1,3] + 7x - x^2/2 [3,7]
= [(2*3^2)-(2*1^2)]+[(7*7-7^2/2)-(7*3-3^2/2)]
= 16+8
= 24

1. 👍 2
2. 👎 4

## Similar Questions

1. ### Calculus

1. The graph of f ′′(x) is continuous and decreasing with an x-intercept at x = –3. Which of the following statements must be true? A. The graph of f is always concave down. B. The graph of f has an inflection point at x =

asked by Justin on July 31, 2019
2. ### Calculus

1. Find the domain for the particular solution to the differential equation dy/dx=3y/x, with initial condition y(1) = 1. A. x > 0 B. x < 0 C. x ≠ 0 D. All real numbers 2. Use geometry to evaluate the integral from negative 2 to

asked by Justin on August 1, 2019
3. ### Calculus AB

Which of the following functions is continuous at x = 3? (5 points) Select one: a. f of x equals the quotient of the quantity x squared minus 9 and the quantity x plus 3 b. f of x equals the quotient of the quantity x squared

asked by Mayur on December 29, 2017
4. ### Calculus

f is a continuous function with a domain [−3, 9] such that f of x equals 3 for x between negative 3 and 0 including negative 3, equals negative 1 times x plus 3 for x between 0 and 6 inclusive, and equals negative 3 for x

asked by Ke\$ha on May 12, 2017
5. ### Calculus

If f(x) and g(x) are continuous on [a, b], which one of the following statements is true? ~the integral from a to b of the difference of f of x and g of x, dx equals the integral from a to b of f of x, dx minus the integral from a

asked by Tiff on March 15, 2016
1. ### geometry

In triangle LM equals 5 and m angle K equals 45. find KL. leave your answer in simplest radical form.?

asked by joana on September 2, 2009
2. ### Macroeconomics

Cannot attach graph! a. If the actual price level exceeds the expected price level reflected in long-term contracts, real GDP equals _______ and the actual price level equals _______ in the short run. b. The situation described in

asked by Amanda on October 24, 2012
3. ### math

Use the formula S equals 2 left-parenthesis l w right-parenthesis plus 2 left-parenthesis l h right-parenthesis plus 2 left-parenthesis w h right-parenthesisto find the surface area of a rectangular prism with the following

asked by kim on March 9, 2018
4. ### geometry

in angle DEF, DF equals 16 and F equals 26. Find FE to the nearest tenth.

asked by gage on May 4, 2011
5. ### Economy

Need help here plz. In a private closed economy, if aggregate expenditures equal GDP, then... A = Consumption equals investment B = Planned investment equals to saving. C = Disposable income equals consumption minus saving D =

asked by George on December 14, 2008