Use limits to find the area between the graph of the function and the x axis given by the definite integral.
∫₁⁵(x²-x+1)dx
Show work

Step-by-step explanation:

Let  

3

4

u

2

=

(

x

−

1

2

)

2

⇒

√

3

2

u

=

x

−

1

2

⇒

√

3

2

d

u

=

d

x

⇒

∫

1

3

4

u

2

+

3

4

⋅

√

3

2

d

u

⇒

√

3

2

∫

1

3

4

(

u

2

+

1

)

d

u

⇒

2

√

3

3

∫

1

u

2

+

1

d

u

Using an antiderivative what should be committed to memory...

⇒

2

√

3

3

tan

−

1

u

+

c

⇒

u

=

2

x

−

1

√

3

⇒

2

√

3

3

tan

−

1

(

2

x

−

1

√

3

)

+

c

ok

step-by-step explanation:

56.6

step-by-step explanation:

the ratio of the perimeters is equal to the scale.

the ratio of the areas is equal to the square of the scale.

34 / 20 = k

a / 19.6 = k²

substituting:

a / 19.6 = (34 / 20)²

a = 19.6 (34 / 20)²

a ≈ 56.6