Consider two functions f and g on [2, 7] such that integral^2 to 7 f(x) dx = 10, integral^2_7 g(x) dx = 7, integral^4_7 f(x) dx = 5, and integral^2_4 g (x) dx = 3. Evaluate the following integrals.
a. integral^5_1 2f(x) dx =
b. integral^8_1 (f(x) - g (x)) dx =
c. integral^5_1 (f (x) - g (x)) dx =
d. integral^8_5 (g(x) - f(x)) dx =
e. integral^8_5 7g(x) dx =
f. integral^1_5 3f(x).

x = 12

y = 15

step-by-step explanation:

cosine

step-by-step explanation:

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true

139 divided by a number

step-by-step explanation: