The Definite integral

The Definite integral

By Sahel Otoom

Multiple Choice

Warm UP(Before)

Find $$\int_{ }^{ }\left(2+\frac{1}{x^2}\right)dx$$  

• $$2x-\frac{1}{x}+c$$  

• $$2x+\frac{1}{x}+c$$  

• $$x^2-\frac{2}{x}+c$$  

The Definite Integral

Multiple Choice

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

• antiderivative

• indefinite integral

• definite integral

• derivative

Multiple Choice

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

• positive

• negative

• zero

Multiple Choice

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

• positive

• negative

• zero

Multiple Choice

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

• positive

• negative

• zero

Multiple Choice

Which of the following is incorrect?

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

• $$\int_a^af\left(x\right)\ dx=0$$  

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

Multiple Choice

$$\int_1^2f\left(x\right)dx=3$$  .  $$\int_1^24f\left(x\right)dx=$$  

• $$12$$  

• $$7$$  

• $$-12$$  

• $$\frac{4}{3}$$  

Multiple Choice

$$\int_0^3g\left(x\right)dx=-5$$  ,  $$\int_3^02g\left(x\right)dx=$$  

• $$-10$$  

• $$10$$  

• $$-7$$  

• $$-\frac{5}{2}$$  

Multiple Choice

If $$\int_1^3\ f\left(x\right)\ dx\ =5,\ \int_1^{11}\ f\left(x\right)\ dx=24$$  and  $$\int_1^3\ g\left(x\right)\ dx=7,$$  evaluate  $$\int_1^3\ 4f\left(x\right)+3g\left(x\right)\ dx$$  

• $$25$$  

• $$41$$  

• $$-1$$  

• $$17$$  

Multiple Choice

If $$\int_1^3\ f\left(x\right)\ dx\ =5,\ \int_1^{11}\ f\left(x\right)\ dx=24$$  and  $$\int_1^3\ g\left(x\right)\ dx=7,$$  evaluate  $$\int_3^{11}\ f\left(x\right)\ dx$$  

• $$-19$$  

• $$41$$  

• $$-11$$  

• $$19$$