Free Printable Definite integrals and its properties

1.

The area under a curve is calculated using which mathematical concept?

a)

antiderivative

b)

indefinite integral

c)

definite integral

d)

derivative

2.

The area under a curve is also known as the ... ?

a)

physical area

b)

algebraic area

c)

integral

d)

antiderivative

3.

The fundamental theorem of calculus is basically:

a)

calculating the area under a curve

b)

$\int_a^b\ f\left(x\right)\ dx=F\left(b\right)-F\left(a\right)$

c)

integrating a function, with no +C

d)

using rectangles to approximate the area under a curve

e)

we didn't learn this!

4.

The result of $\int_1^3\left(x-2\right)\ dx$ is:

a)

positive

b)

negative

c)

zero

5.

The result of $\int_0^2\left(x^2-2x+1\right)\ dx$ is:

a)

positive

b)

negative

c)

zero

6.

The result of $\int_0^2\left(x^3-2x^2-x+1\right)\ dx$ is:

a)

positive

b)

negative

c)

zero

7.

The shaded area in the figure is represented by which of the following integral expressions?

a)

$\int_{-1}^2f\left(x\right)\ dx$

b)

$-\int_2^{-1}f\left(x\right)\ dx$

c)

$-\int_{-1}^2f\left(x\right)\ dx$

d)

$\int_{-2}^1f\left(x\right)\ dx$

8.

The shaded area shown in the figure can be represented by which of the following integral expressions?

a)

$\int_0^3f\left(x\right)\ dx$

b)

$-\int_0^1f\left(x\right)\ dx+\int_1^3f\left(x\right)\ dx$

c)

$\int_0^1f\left(x\right)\ dx+\int_1^3f\left(x\right)\ dx$

d)

$\int_1^0f\left(x\right)\ dx+\int_1^3f\left(x\right)\ dx$

9.

Considering the area shown in the diagram, which of the following statements is not true?

a)

The algebraic area could be negative.

b)

The physical area is positive.

c)

Both the physical area and algebraic area could be negative.

d)

Both the physical area and algebraic area could be positive.

10.

The area under a curve can be represented by $\int_a^bf\left(x\right)\ dx$ only if:

a)

$f\left(x\right)$ is positive

b)

$f\left(x\right)$ is continuous

c)

$f\left(a\right)$ exists

d)

$f\left(b\right)$ exists

11.

Which of the following is incorrect?

a)

$\int_b^af\left(x\right)\ dx=-\int_a^bf\left(x\right)\ dx$

b)

$\int_a^af\left(x\right)\ dx=0$

c)

$\int_a^bf\left(x\right)\ dx+\int_b^cf\left(x\right)\ dx$
$=\int_a^cf\left(x\right)\ dx$

d)

$\int_a^bf\left(x\right)\ dx-\int_b^cg\left(x\right)\ dx$
$=\int_a^c\left(f\left(x\right)-g\left(x\right)\right)\ dx$

e)

$\int_a^bf\left(x\right)\ dx-\int_a^bg\left(x\right)\ dx$
$=\int_a^b\left(f\left(x\right)-g\left(x\right)\right)\ dx$

Definite integrals and its properties

Total questions: 11

Worksheet time: 8mins

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