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study help
mathematics
precalculus

Questions and Answers of Precalculus

Evaluate the integral. x' + 2x? + 3x – 2 .3 dx (x² + 2x + 2)?
Evaluate the integral. х? — Зх + 7 (x² ? — 4х + 6)?
Evaluate the integral. x* + 3x? + 1 .2 dx .5 x* + 5x + 5x .3
Evaluate the integral. 5x* + 7x? + x + 2 dx x(x² + 1)?
Evaluate the integral. x* + x – 1 x³ + 1 .3
Evaluate the integral. x' + 2x dx Jo x* + 4x2 + 3
Evaluate the integral. dx Jo ²+ 4x + 13 х
Evaluate the integral. x³ – 2x? + 2x – 5 dx x* + 4x? + 3 4
Evaluate the integral. x + 4 dx x? + 2x + 5
Evaluate the integral. х3 + 6х — 2 dx .4 x* + 6x?
Evaluate the integral. x' + 4x + 3 x* + 5x? + 4 .4
Evaluate the integral. x? + x + 1 (x² + 1)?
Evaluate the integral. 4x dx x' + x? + x + 1 .3
Evaluate the integral. x? – x + 6 dx x' + 3x
Evaluate the integral. 10 dx (x – 1)(x² + 9)
Evaluate the integral. x* + 9x? + x + 2 =dx x? + 9
Evaluate the integral. dt (1² – 1)?
Evaluate the integral. '3 x(3 — 5х) dx (Зх — 1)(х — 1)?
Evaluate the integral. x? + x + 1 (x + 1)(x + 2)
Evaluate the integral. Зx? + 6х + 2 '2 dx .2 х2 + 3x + 2
Evaluate the integral. ,2 12 4y2 – 7y – 12 dy У(у + 2)(у — 3)
Evaluate the integral. – 1 (2 x' + 4x? + .3 .2 x³ + x?
Evaluate the integral. х3 — 4х + 1 .3 Со dx - x? — Зх + 2
Evaluate the integral. dx (x + a)(x + b)
Evaluate the integral. ах -dx J x? – bx
Evaluate the integral. х — 4 x? — 5х + 6
Evaluate the integral. Jo 2x + 3x + 1 dx
Evaluate the integral. dy (y + 4)(2y – 1)
Evaluate the integral. 5х + 1 dx (2х + 1)(х — 1)
Evaluate the integral. 3t – 2 dt t + 1
Evaluate the integral. х* х х— 1
Write out the form of the partial fraction decomposition of the function (as in Example 7). Do not determine the numerical values of the coefficients.(a)(b)Image caption .2 – 4 x* (x? – x +
Write out the form of the partial fraction decomposition of the function (as in Example 7). Do not determine the numerical values of the coefficients.(a)(b) x* – 2x + x? + 2x – 1 x² – 2x + 1
Write out the form of the partial fraction decomposition of the function (as in Example 7). Do not determine the numerical values of the coefficients.(a)(b) x2 + x*
Write out the form of the partial fraction decomposition of the function (as in Example 7). Do not determine the numerical values of the coefficients.(a)(b) х — 6 x? + x – 6 .2 х x? .2 .2
Write out the form of the partial fraction decomposition of the function (as in Example 7). Do not determine the numerical values of the coefficients.(a)(b) 4 + x (1 + 2x)(3 – x) х + x* .3 4
The parabola y = 1/2 x2 divides the disk x2 + y2 < 8 into two parts. Find the areas of both parts.
Find the volume of the solid obtained by rotating about the line x = 1 the region under the curvey = x√1 - x2 , 0 < x < 1.
Find the area of the region bounded by the hyperbola 9x2 - 4y2 = 36 and the line x = 3.
Evaluate(a) By trigonometric substitution.(b) By the hyperbolic substitution x = a sinh t. x? (x² + a²)³/2
Evaluate the integral. cos t = dt w/2 V1 + sin²t
Evaluate the integral. Jx/T- xª dx
Evaluate the integral. x? + 1 (x² – 2x + 2)²
Evaluate the integral. | Vx? + 2x dx
Evaluate the integral. x2 dx (3 + 4x – 4x²)³/2
Evaluate the integral. |x V3 + 2x – x² dx x?.
Evaluate the integral. /x – x² dx
Evaluate the integral. dx -2 x² + 2x + 5
Evaluate the integral. Vx² + 1 dx
Evaluate the integral. r0.6 x2 dx V9 – 25x²
Evaluate the integral. х -dx /1 + x²
Evaluate the integral. /1 + x² dx
Evaluate the integral. dx 12 [(ах)? — ь?]2
Evaluate the integral. dx. Vx² – 7
Evaluate the integral. dx (2/3 J.u2/3 x°/9x² – 1
Evaluate the integral. x'Va? – x² dx
Evaluate the integral. dx (x² + 1)²
Evaluate the integral. Vx2 x² – 9 dx x3
Evaluate the integral. dt *2 V4 + t?
Evaluate the integral. r1/2 х V1— 4х? dx Сx— 4x7
Evaluate the integral. *2/3 4 — 9х? dx
Evaluate the integral. dx C3 (x² – 1)3/2 12
Evaluate the integral. dt tVt? – 16
Evaluate the integral. dx 'a a > 0 (a² + x²)³/2*
Evaluate the integral. '3 dx V36 – x2
Evaluate the integral. V? – 1 Vx² dx
Evaluate the integral. x2 dx 9 – x²
Evaluate the integral using the indicated trigonometric substitution. Sketch and label the associated right triangle. .3 = dx x = 2 tan 0 -2 /x² + 4
A finite Fourier series is given by the sum= a1 sin x + a2 sin 2x + ∙ ∙ ∙ + aN sin Nx Show that the mth coefficient am is given by the formula f(x) = E a, sin nx n=1
Find the volume obtained by rotating the region bounded by the curves about the given axis.y = sin x, y = cos x, 0 < x < π/3; about y = 1
Find the volume obtained by rotating the region bounded by the curves about the given axis.y = sin x, y = cos x, 0 < x < π/4; about y = 1
Find the volume obtained by rotating the region bounded by the curves about the given axis.y = sin2 x, y = 0, 0 < x < π; about the x-axis
Use a graph of the integrand to guess the value of the integral. Then use the methods of this section to prove that your guess is correct. 22 sin 2тx сos 5пхdx
Use a graph of the integrand to guess the value of the integral. Then use the methods of this section to prove that your guess is correct. cosx dx
Find the area of the region bounded by the given curves. tan?x, , 0
Find the area of the region bounded by the given curves. sin?x, y = sin³x, 0
Evaluate the indefinite integral. Illustrate, and check that your answer is reasonable, by graphing both the integrand and its antiderivative (taking C = 0). sec*(;x) dx dл
Evaluate the indefinite integral. Illustrate, and check that your answer is reasonable, by graphing both the integrand and its antiderivative (taking C = 0). sin 3x sin 6x dx
Evaluate the indefinite integral. Illustrate, and check that your answer is reasonable, by graphing both the integrand and its antiderivative (taking C = 0). sin'x cosx dx
Evaluate the indefinite integral. Illustrate, and check that your answer is reasonable, by graphing both the integrand and its antiderivative (taking C = 0). x sin?(x²) dx ||
If ∫π/40 tan6x sec x dx = I, express the value of ∫π/40 tan8x sec x dx in terms of I.
Evaluate the integral. *T/2 csc*0 cot*0 d0 7/4
Evaluate the integral.
Evaluate the integral. x tan?x dx
Evaluate the integral. dx 1 cos x –
Evaluate the integral. 1 – tan²x secʻx
Evaluate the integral. °T/4 (1 cos 40 de
Evaluate the integral. 1 + cos 2x dx
Evaluate the integral. sin x sec'x dx
Evaluate the integral. 1/2 cos 5t cos 10t dt
Evaluate the integral. sin 20 sin 60 de
Evaluate the integral. sin 8x cos 5x dx
Evaluate the integral.
Evaluate the integral. csc x dx
Evaluate the integral.
Evaluate the integral. X sec x tan x dx
Evaluate the integral. tan sec x dx
Evaluate the integral. tan'x dx
Evaluate the integral. T/4 tan*t dt * 0,
Evaluate the integral. tan'x sec'x dx

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