Start learning →

AP Intermediate 2nd Year Integrals and Applications — practice questions — page 4

Explore 121 free Integrals and Applications questions in AP Intermediate 2nd Year Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

Practise Integrals and Applications with Quill →

Integrals and Applications questions and exercises with answers

Showing questions 91–120 of 121.

The AREA bounded by y = x² and the x-axis from x = 0 to x = 3 is:Read the answer and worked solution →The improper integral ∫_1^∞ (1/x²) dx evaluates to:Read the answer and worked solution →The integral ∫ x^n dx (for n ≠ -1) equals:Read the answer and worked solution →When the integral is negative, the area is taken as its:Read the answer and worked solution →The area of one thin strip is called the:Read the answer and worked solution →Strips used to find an area may be vertical or:Read the answer and worked solution →Only the numerical value of an area is taken into consideration, so signs are:Read the answer and worked solution →The width of an elementary vertical strip is written as:Read the answer and worked solution →Application of integrals bingoRead the answer and worked solution →Pick the right expressionRead the answer and worked solution →Vertical or horizontal strip?Read the answer and worked solution →Complete the area ruleRead the answer and worked solution →Spot the odd one outRead the answer and worked solution →For a horizontal strip, the elementary area would be:Read the answer and worked solution →The height of a vertical elementary strip is given by:Read the answer and worked solution →An elementary area is located at a position specified by some value of:Read the answer and worked solution →The area under a curve is built from a large number of thin:Read the answer and worked solution →For a vertical strip of height y and width dx, dA equals:Read the answer and worked solution →The definite integral is evaluated using which theorem?Read the answer and worked solution →Areas are found here for lines and arcs of circles, plus:Read the answer and worked solution →The definite integral was first defined as the limit of:Read the answer and worked solution →The total area comes from adding up all the:Read the answer and worked solution →Match the area termRead the answer and worked solution →If a curve lies below the x-axis, its integral comes out:Read the answer and worked solution →Properties in useRead the answer and worked solution →Two are true, one is notRead the answer and worked solution →Which process is being described?Read the answer and worked solution →For the region below the axis A1 is negative while A2 is:Read the answer and worked solution →True or false about areasRead the answer and worked solution →Finding the area of a circle here uses which curves in standard form?Read the answer and worked solution →

Worked practice questions

The AREA bounded by y = x² and the x-axis from x = 0 to x = 3 is:

  1. $3$ (using only the upper limit)
  2. $6$ (twice the upper limit value)
  3. $9$ (using anti-derivative properly)
  4. $27$ (cubing the upper limit)
Show answer and solution

Correct answer: C. $9$ (using anti-derivative properly)

Area = ∫_0^3 x² dx = [x³/3] from 0 to 3 = 27/3 − 0 = 9.

Open this question →

The improper integral ∫_1^∞ (1/x²) dx evaluates to:

  1. Infinity (diverges, like harmonic series)
  2. $0$ (vanishes at boundary)
  3. $2$ (twice the converged value)
  4. $1$ (converges to a finite value)
Show answer and solution

Correct answer: D. $1$ (converges to a finite value)

∫_1^∞ x^(-2) dx = [-1/x] from 1 to ∞ = 0 − (-1) = 1. Converges. Compare ∫_1^∞ (1/x) dx = ∞ (diverges, harmonic case).

Open this question →

The integral ∫ x^n dx (for n ≠ -1) equals:

  1. $n x^{n-1} + C$ (derivative formula)
  2. $x^{n+1} + C$ (missing divisor)
  3. $x^n + C$ (no change)
  4. $x^{n+1} / (n+1) + C$ (power rule)
Show answer and solution

Correct answer: D. $x^{n+1} / (n+1) + C$ (power rule)

Power rule for integration: ∫x^n dx = x^(n+1)/(n+1) + C, valid for n ≠ -1. For n = -1, ∫(1/x)dx = ln|x| + C.

Open this question →

How to practise

  1. Choose a Integrals and Applications question and try to work out your answer.
  2. Open the question to check the correct answer and read its worked solution.
  3. Continue in the app for bite-sized lessons, explanations and review with Quill. You can start without creating an account.

Put it into practice

Continue with Integrals and Applications practice for AP Intermediate 2nd Year. Read explanations as you go. No signup form needed to start.

Practise Integrals and Applications →

More Mathematics topics

Vector Algebra and 3D GeometryContinuity, Differentiability & DerivativesLinear ProgrammingRelations, Functions & Inverse TrigonometryDifferential EquationsDeterminantsMatrices and DeterminantsProbability