AP Calculus BC Techniques of Integration — practice questions
22 free MCQs with worked solutions. Tap any question for the answer + explanation, or practice them all in the app.
Practice AP Calculus BC Techniques of Integration in the app →A student asks whether integration has its own product rule. The honest answer is that there:Instead, a technique built on the differentiation product rule swaps one integral for another. That technique Deciding which factor to call u, a student uses a memory aid ordering logarithmic, inverse, algebraic, trigonoAn integrand holds an algebraic function and a trigonometric one. Under that ordering, u should be the:After finding an antiderivative, a student can confirm it is right by:An integral involving a square root of a quadratic often yields to a technique using sine, tangent or secant. To integrate a rational function, a student splits it into simpler fractions. That method is:The exact form that decomposition takes depends heavily on the factorisation of the:A definite integral was first defined as the limit of sums built on rectangles. Those sums are:Approximating an integral with rectangles whose heights come from the centre of each subinterval uses the:A method that approximates the region with parabolic arcs rather than straight tops is:Comparing an estimate with the true value gives two quantities: relative error and:Before computing, a student wants to know how far off an estimate could be. A theorem supplies error:An integral runs all the way to infinity, or the integrand blows up inside the interval. Such integrals are caOne kind of such integral is taken over an interval that is:The other kind is taken over a closed interval where the function has an infinite:Evaluating such an integral, a student finds the limit does not exist. The integral is then said to:When the limit does exist and gives a finite value, the integral is said to:Some improper integrals cannot be evaluated directly, so a student compares them with a chosen integral. That Integration by parts also has a version adapted for use with:Before choosing a technique, a student must first recognise when integration by parts is:For a rational function, the first thing to recognise is the presence of simple: