Finding the Value of an Integral with U-Substitution

[Zack K]

Homework Statement

Suppose that: ₀∫²f(x)dx = 2 ₁∫²f(x)dx = -1 and ₂∫⁴ = 7, find ₀∫¹f(x+1)dx

Homework Equations

_a∫^bf(x) = F(b) - F(a)

The Attempt at a Solution

So in these types of integration, we are needed to use u-substitution, the problem is, using u-substitution requires you to have the equation of the graph to get an exact value, but we just have f(x).I already evaluated ₀∫¹f(x)dx = 3 if that helps at all.

 

[PeroK]

Homework Statement

Suppose that: ₀∫²f(x)dx = 2 ₁∫²f(x)dx = -1 and ₂∫⁴ = 7, find ₀∫¹f(x+1)dx

Homework Equations

_a∫^bf(x) = F(b) - F(a)

The Attempt at a Solution

So in these types of integration, we are needed to use u-substitution, the problem is, using u-substitution requires you to have the equation of the graph to get an exact value, but we just have f(x).I already evaluated ₀∫¹f(x)dx = 3 if that helps at all.

I don't understand your problem with a simple substitution. Why do you think you can't substitute here?

 

[Mark44]

Homework Statement

Suppose that: ₀∫²f(x)dx = 2 ₁∫²f(x)dx = -1 and ₂∫⁴ = 7, find ₀∫¹f(x+1)dx

Without punctuation, he line above took me a while to figure out. At first I thought this meant $\int_0^2 f(x)dx = 2 \cdot \int_1^2 f(x)dx = -1$. IOW that the values of the two integrals were -1 and -1/2, respectively.

Homework Equations

_a∫^bf(x) = F(b) - F(a)

The Attempt at a Solution

So in these types of integration, we are needed to use u-substitution, the problem is, using u-substitution requires you to have the equation of the graph to get an exact value, but we just have f(x).I already evaluated ₀∫¹f(x)dx = 3 if that helps at all.

No, you don't need the equation of the function (f in this case). Just do a substitution and see what you get.