Lesson 8.1.1
8.1.1 Fundamental Theorem of calculus and integration as reverse differentiation Quiz: Pearson Edexcel Maths, Unit 8
20 questions
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Lesson 8.1.1, Fundamental Theorem of calculus and integration as reverse differentiation: 20 multiple choice questions for the Pearson Edexcel Maths (9MA0), Unit 8: Integration, written with Revision Ninja.
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The 20 questions
-
What mathematical operation is the direct inverse of differentiation in calculus?
- Substitution
- Integration
- Factorisation
- Logarithm
-
Which theorem links the evaluation of definite integrals to antiderivatives?
- Remainder Theorem
- Fundamental Theorem
- Binomial Theorem
- Factor Theorem
-
What must be included when finding the general indefinite integral of a function?
- Zero boundary
- Constant of integration
- Derivative term
- Upper limit
-
If f dash of x equals 2x, what is the indefinite integral of f dash of x?
- 2x squared plus c
- x squared
- 2
- x squared plus c
-
What is the result of differentiating the indefinite integral of a continuous function?
- Unity
- Zero
- Its second derivative
- The original function
-
What is the integral of the constant 5 with respect to x?
- 5x plus c
- 5
- zero
- 5 plus c
-
Which term describes a function whose derivative is the given function?
- Antiderivative
- Asymptote
- Coefficient
- Reciprocal
-
Evaluate the definite integral from 1 to 3 of 2x dx.
- 10
- 8
- 4
- 12
-
What is the integral of x to the power minus two with respect to x?
- x⁻¹
- -2x⁻³
- -x⁻²
- -x⁻¹
-
What is the integral of 1 over x with respect to x for positive x?
- ln x
- 1 over x squared
- minus 1 over x squared
- e to the x
-
If the integral from a to b of f of x dx equals 5, what does the integral from b to a equal?
- 5
- 0
- minus 5
- 25
-
What is the integral of e to the power 2x with respect to x?
- quarter e to the 2x
- 2e to the 2x
- e to the 2x
- half e to the 2x
-
What is the antiderivative of cos x?
- cos x
- minus sin x
- minus cos x
- sin x
-
What is the integral of sin x with respect to x?
- cos x
- minus sin x
- sin x
- minus cos x
-
If f of x equals x squared, what is the net area under f of x from x equals 0 to 3?
- 27
- 4.5
- 3
- 9
-
Which integration technique is the reverse of the chain rule?
- Numerical integration
- Partial fractions
- Integration by parts
- Integration by substitution
-
What does evaluating a definite integral geometrically represent under the curve?
- Arc length
- Signed area
- Total gradient
- Maximum value
-
What is the indefinite integral of the function three x squared with respect to x?
- six x plus c
- x cubed
- x cubed plus c
- three x cubed plus c
-
What is the value of the definite integral from zero to one of four x cubed dx?
- four
- one quarter
- zero
- one
-
What is the integral of seven over x with respect to x for positive x?
- ln x + c
- 7 ln x + c
- ln 7x + c
- 7x⁻¹ + c
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