Integral Questions with Solutions: Practice and Master Integration

Calculate this triple integral over D:
$\int \int \int \sqrt{10 + y^{2} - x^{2}} d x d y d z$
over the region bounded D:
$D = {(x, y, z) ∣ x^{2} + z^{2} \leq y^{2} + 10, x^{2} + y^{2} \leq 9}$

villane0 2021-11-12

Let $F (x, y, z) = ξ + y j + z k$ . Evaluate the integral of F alomg each of the following paths.
$c (t) = (t, t, t), 0 \leq t \leq 3$

smellmovinglz 2021-11-12

For a certain incompressible, two-dimensional flow field the velocity component in the y direction is given by the equation
$v = 3 x y + x^{2} y$
Determine the velocity component in the x direction so that the volumetric dilatation rate is zero.

Travis Fogle 2021-11-12

Evaluate the line integral after converting it to an ordinary integral with respect to the parameter.
$\int_{C} (y - z) d s$
C is the helix $r (t) = < 3 \cos t, 3 \sin t, t >$ , for $0 \leq t \leq 2 π$

gonjenjemeb 2021-11-12

Use the Integral Test to determine whether the series is convergent or divergent.
$\sum_{n = 1}^{\infty} \frac{n}{n^{2} + 1}$

allhvasstH 2021-10-27

Evaluate the integrals.
$\int_{2}^{3} \frac{x^{2} + 2 x - 2}{x^{3} + 3 x^{2} - 6 x} d x$

avissidep 2021-10-27

Find the area of the surface. The surface $z = \frac{2}{3} (\frac{x^{3}}{2} + \frac{y^{3}}{2}), 0 \leq x \leq 1$

sagnuhh 2021-10-27

Evaluate the integrals
$\int_{1}^{8} \frac{\log_{4} θ}{θ} d θ$

Jaden Easton 2021-10-27

Evaluate the integrals.
$\int_{0}^{2} {(2 x + 1)}^{3} d x$

ossidianaZ 2021-10-26

Evaluate the surface integral
$\int \int_{S} (x^{2} z + y^{2} z) d s$
where S is the hemisphere $x^{2} + y^{2} + z^{2} = 9, z \geq 0$

tricotasu 2021-10-26

Evaluate the integrals
$\int \frac{1}{x} {(1 + 7 \ln x)}^{- \frac{1}{3}} d x$

Sinead Mcgee 2021-10-25

Evaluate the integrals.
$\int_{1}^{e} \frac{d x}{x + \ln x}}$

Mylo O'Moore 2021-10-25

A flat, square surface with side length 3.40 cm is in the xy-plane at z = 0. Calculate the magnitude of the flux through this surface produced by a magnetic field $\vec{B} = (0.200 T) \hat{i} + (0.300 T) \hat{j} - (0.500 T) \hat{k}$

Rui Baldwin 2021-10-25

Find the volume of the given solid Bounded by the coordinate planes and the plane 3x+2y+z=6

sodni3 2021-10-25

Evaluate the integrals.
$\int_{0}^{1} x \cdot 2^{x^{2} + 1} d x$

babeeb0oL 2021-10-24

Evaluate the integrals
$\int_{0}^{\frac{π}{4}} [\sec t i + \tan^{2} t j - t \sin t k] d t$

chillywilly12a 2021-10-24

Evaluate the integrals.
$\int_{1}^{4} (\frac{\sqrt{v} + v}{v}) d v$

he298c 2021-10-24

Evaluate the integrals.
$\int_{- 5}^{5} \frac{w^{3}}{\sqrt{w^{50} + w^{20} + 1}}$

Cabiolab 2021-10-23

Evaluate the following integrals. Include absolute values only when needed.
$\int \frac{d x}{x \ln x (\ln x)}$

Mylo O'Moore 2021-10-23

Find the indefinite integrals (most general antiderivatives). You may need to try a solution and then adjust your guess. Check your answers by differentiation.
$\int x^{3} {(1 + x^{4})}^{\frac{- 1}{4}} d x$

Although solving integrals starts in high school, these answers that are provided are related to post-secondary problems that are approached by Data Science students, economists, and engineers in their daily tasks. It’s a reason why integral questions that you will see below will span across a wide range of problems. You can also compare your integral problem and see equations that relate to your question. Alternatively, it will help you with solving integrals step by step. There are many methods to do that as the provided answers show. Starting with solving integrals with substitution to variables, the help is there.

Integral Calculus

Integral Problem Solving Made Easy: Learn with Examples