The portal has been deactivated. Please contact your portal admin.

Lesson Worksheet: Antiderivatives Mathematics • 12th Grade

In this worksheet, we will practice finding the antiderivative of a function. The antiderivative of a function f(x) is the function F(x) where F′(x) = f(x).

Q1:

Find the most general antiderivative 𝐹(𝑥) of the function 𝑓(𝑥)=3𝑥2𝑥1.

  • A𝐹(𝑥)=3𝑥2𝑥𝑥+C
  • B𝐹(𝑥)=𝑥+𝑥𝑥+C
  • C𝐹(𝑥)=𝑥+𝑥+𝑥+C
  • D𝐹(𝑥)=𝑥𝑥𝑥+C
  • E𝐹(𝑥)=9𝑥4𝑥𝑥+C

Q2:

Find the most general antiderivative 𝐹(𝑥) of the function 𝑓(𝑥)=2𝑥3𝑥𝑥.

  • A𝐹(𝑥)=𝑥+𝑥+𝑥+C
  • B𝐹(𝑥)=2𝑥3𝑥𝑥+C
  • C𝐹(𝑥)=16𝑥18𝑥3𝑥+C
  • D𝐹(𝑥)=𝑥4𝑥2𝑥3+C
  • E𝐹(𝑥)=𝑥8+𝑥6+𝑥3+C

Q3:

Determine the most general antiderivative 𝐹(𝑥) of the function 𝑓(𝑥)=2𝑥+3𝑥𝑥.

  • A𝐹(𝑥)=10𝑥3+6𝑥5+C
  • B𝐹(𝑥)=6𝑥5+6𝑥5+C
  • C𝐹(𝑥)=2𝑥+3𝑥+C
  • D𝐹(𝑥)=3𝑥+9𝑥2+C
  • E𝐹(𝑥)=2𝑥+3𝑥+C

Q4:

Find the most general antiderivative of the function 𝑓(𝑥)=4𝑥+323𝑥sin.

  • A𝐹(𝑥)=4𝑥3+3𝑥4𝑥+cosC
  • B𝐹(𝑥)=2𝑥3+3𝑥4𝑥+cosC
  • C𝐹(𝑥)=4𝑥+3𝑥4𝑥+cosC
  • D𝐹(𝑥)=2𝑥3+3𝑥+4𝑥+cosC
  • E𝐹(𝑥)=4𝑥3+3𝑥+4𝑥+cosC

Q5:

If 𝐹(𝑥) and 𝐹(𝑥) are both antiderivatives of the same function 𝑓(𝑥), what is the relation between 𝐹 and 𝐹?

  • A𝐹 must be the double of 𝐹.
  • B𝐹𝐹 is a constant.
  • C𝐹 must be equal to 𝐹.
  • D𝐹+𝐹 must be a constant.
  • EOnly one of them is undefined.

Q6:

By considering the product rule, find a function 𝑓 so that 𝑓(𝑥)=𝑒𝑥+2𝑒𝑥.

  • A𝑓(𝑥)=2𝑥𝑒+C
  • B𝑓(𝑥)=2𝑒𝑥+C
  • C𝑓(𝑥)=𝑥𝑒+C
  • D𝑓(𝑥)=𝑒𝑥+C
  • E𝑓(𝑥)=2𝑥𝑒+C

Q7:

If 𝑓(𝑥)=3𝑥+3𝑥+5𝑥+2, determine 𝑓(𝑥).

  • A𝑓(𝑥)=𝑥2+3𝑥4+5𝑥2+2𝑥+C
  • B𝑓(𝑥)=3𝑥+3𝑥+5𝑥+2𝑥+C
  • C𝑓(𝑥)=3𝑥+3𝑥+5𝑥+2𝑥+𝑥+CD
  • D𝑓(𝑥)=3𝑥4+3𝑥2+C
  • E𝑓(𝑥)=𝑥14+3𝑥20+5𝑥6+𝑥+𝑥+CD

Q8:

Determine 𝑓(𝑡) if 𝑓(𝑡)=4𝑡+5𝑡cos.

  • A𝑓(𝑡)=32𝑡1055𝑡+𝑡+sinCD
  • B𝑓(𝑡)=32𝑡1055𝑡+𝑡+𝑡+sinCDE
  • C𝑓(𝑡)=32𝑡1055𝑡+𝑡+sinCE
  • D𝑓(𝑡)=8𝑡3+5𝑡+sinC
  • E𝑓(𝑡)=16𝑡155𝑡+𝑡+cosCD

Q9:

Determine the antiderivative 𝐹 of the function 𝑓(𝑥)=5𝑥+4𝑥 where 𝐹(1)=2.

  • A𝐹(𝑥)=5𝑥+4𝑥11
  • B𝐹(𝑥)=𝑥+𝑥3
  • C𝐹(𝑥)=𝑥+𝑥4
  • D𝐹(𝑥)=5𝑥+4𝑥+94
  • E𝐹(𝑥)=𝑥+𝑥+17

Q10:

Determine the function 𝑓 if 𝑓(𝑥)=3𝑥+1𝑥 and 𝑓(1)=4.

  • A𝑓(𝑥)=9𝑥2+2𝑥+4
  • B𝑓(𝑥)=2𝑥+2𝑥+4
  • C𝑓(𝑥)=2𝑥+2𝑥+13
  • D𝑓(𝑥)=9𝑥2+2𝑥+13
  • E𝑓(𝑥))=2𝑥+2𝑥4

This lesson includes 25 additional questions and 252 additional question variations for subscribers.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.