AQA alevel maths topic 16- integration Flashcards
What is the integral of x^n with respect to x?
The integral is (x^(n+1))/(n+1) + C, where n ≠ -1.
True or False: The integral of a constant k with respect to x is kx + C.
True.
What is the integral of sin(x)?
-cos(x) + C.
Fill in the blank: The process of finding the integral of a function is called ______.
integration.
What is the integral of e^x?
e^x + C.
Define the term ‘definite integral’.
A definite integral is an integral with upper and lower limits, representing the area under the curve between those limits.
What is the Fundamental Theorem of Calculus?
It states that differentiation and integration are inverse processes.
What is the integral of cos(x)?
sin(x) + C.
True or False: The integral of 1/x is ln|x| + C.
True.
What is the purpose of the constant C in indefinite integrals?
It represents the family of antiderivatives.
What is the notation for the definite integral from a to b of f(x)?
∫[a, b] f(x) dx.
Calculate the integral of x^2 from 1 to 3.
The result is 8/3.
What is the integration by parts formula?
∫u dv = uv - ∫v du.
True or False: The area under a curve can be calculated using definite integrals.
True.
What is the integral of tan(x)?
-ln|cos(x)| + C.
Fill in the blank: The integral of a function f(x) from a to b is equal to the ______ of f(x) between those limits.
net area.
What is the integral of a function that is piecewise defined?
You must integrate each piece over its respective interval and sum the results.
What does the symbol ∫ signify?
It signifies integration.
What is the integral of 1/(1 + x^2)?
arctan(x) + C.
What is the method to evaluate the integral of a polynomial function?
Apply the power rule for integration.
True or False: Indefinite integrals yield a single numeric value.
False.
What is the integral of sec^2(x)?
tan(x) + C.
What is the purpose of using substitution in integration?
To simplify the integral into a more manageable form.
What is the integral of 3x^2 + 2x + 1?
x^3 + x^2 + x + C.
