Math  /  Calculus

QuestionSelect the correct answer.
If the area (in square units) of the region under the curve of the function f(x)=4f(x)=4 on the interval [1,a][1, a] is 20 square units, and a>1a>1, then what is the value of aa ? A. 5 B. 6 C. 8 D. 9

Studdy Solution

STEP 1

1. The function f(x)=4 f(x) = 4 is a constant function.
2. The area under the curve is calculated using definite integration.
3. The interval is [1,a][1, a] with a>1a > 1.
4. The area under the curve is given as 2020 square units.

STEP 2

1. Recall the formula for the area under a constant function.
2. Set up the equation for the area.
3. Solve for aa.

STEP 3

Recall the formula for the area under a constant function f(x)=c f(x) = c over an interval [b,a][b, a]:
Area=c×(ab) \text{Area} = c \times (a - b)

STEP 4

Set up the equation for the area using the given function f(x)=4 f(x) = 4 and the interval [1,a][1, a]:
4×(a1)=20 4 \times (a - 1) = 20

STEP 5

Solve for aa:
4×(a1)=20 4 \times (a - 1) = 20 a1=204 a - 1 = \frac{20}{4} a1=5 a - 1 = 5 a=5+1 a = 5 + 1 a=6 a = 6
The value of aa is:
6 \boxed{6}

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