(05.02)If the integral from 2 to 5 of f of x, dx equals 4 and the integral from 2 to 7 of f of x, dx equals negative 3, then what is the value of integral from 5 to 7 of f of x, dx?
–12
–7
7
–1
To find the value of the integral from 5 to 7 of f(x)dx, we can use the property of linearity of integrals.
The property states that if we have two functions f(x) and g(x) and constants a and b, then the integral of the sum of af(x) and bg(x) is equal to the sum of the integrals of af(x) and bg(x), respectively.
In this case, we can rewrite the integral from 5 to 7 of f(x)dx as the sum of two integrals: the integral from 2 to 7 and the integral from 2 to 5 of f(x)dx.
Using the property of linearity, we can write:
∫[5 to 7] f(x)dx = ∫[2 to 7] f(x)dx - ∫[2 to 5] f(x)dx
Given that the integral from 2 to 7 of f(x)dx equals -3 and the integral from 2 to 5 of f(x)dx equals 4, we can substitute these values into the equation:
∫[5 to 7] f(x)dx = -3 - 4
Simplifying the expression, we get:
∫[5 to 7] f(x)dx = -7
So, the value of the integral from 5 to 7 of f(x)dx is -7.
huh?
-3 = 4 + x
You solved 3 = 4+x
o ok
well,
∫[2,7] = ∫[2,5] + ∫[5,7]
so, ...