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Math Calculus Calculus: Early Transcendentals (3rd Edition)

Definite integrals Use a change of variables or Table 5.6 to evaluate the following definite integrals. 58. ∫ 0 π / 4 sin θ cos 3 θ d θ

Definite integrals Use a change of variables or Table 5.6 to evaluate the following definite integrals. 58. ∫ 0 π / 4 sin θ cos 3 θ d θ

Solution Summary: The author evaluates the value of the definite integral by using the change of variable method or Table 5.6.

Calculus: Early Transcendentals (3rd Edition)

Calculus: Early Transcendentals (3rd Edition)

3rd Edition

ISBN: 9780134770468

Author: Briggs

Publisher: PEARSON

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Chapter 5.5, Problem 58E

Definite integrals Use a change of variables or Table 5.6 to evaluate the following definite integrals.

58. ∫ 0 π / 4 sin θ cos 3 θ d θ

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Chapter 5.5, Problem 57E

Chapter 5.5, Problem 59E

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Calculus: Early Transcendentals (3rd Edition)

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Population models The population of a culture of...Ch. 5.5 - Variations on the substitution method Evaluate the...Ch. 5.5 - Variations on the substitution method Find the...Ch. 5.5 - Variations on the substitution method Find the...Ch. 5.5 - Variations on the substitution method Find the...Ch. 5.5 - Variations on the substitution method Find the...Ch. 5.5 - Variations on the substitution method Find the...Ch. 5.5 - Variations on the substitution method Find the...Ch. 5.5 - x(x+10)9dx Ch. 5.5 - 033dx9+x2 Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Integrals with sin2 x and cos2 x Evaluate the...Ch. 5.5 - Prob. 94E Ch. 5.5 - Explain why or why not Determine whether the...Ch. 5.5 - Prob. 96E Ch. 5.5 - Prob. 97E Ch. 5.5 - Areas of regions Find the area of the following...Ch. 5.5 - Prob. 99E Ch. 5.5 - Prob. 100E Ch. 5.5 - Substitutions Suppose that p is a nonzero real...Ch. 5.5 - Prob. 102E Ch. 5.5 - Average value of sine functions Use a graphing...Ch. 5.5 - Equal areas The area of the shaded region under...Ch. 5.5 - Equal areas The area of the shaded region under...Ch. 5.5 - Prob. 106E Ch. 5.5 - Prob. 107E Ch. 5.5 - Prob. 108E Ch. 5.5 - More than one way Occasionally, two different...Ch. 5.5 - Prob. 110E Ch. 5.5 - Prob. 111E Ch. 5.5 - sin2 ax and cos2 ax integrals Use the Substitution...Ch. 5.5 - Integral of sin2 x cos2 x Consider the integral...Ch. 5.5 - Substitution: shift Perhaps the simplest change of...Ch. 5.5 - Prob. 115E Ch. 5.5 - Prob. 116E Ch. 5.5 - Prob. 117E Ch. 5.5 - Prob. 118E Ch. 5.5 - Multiple substitutions If necessary, use two or...Ch. 5 - Explain why or why not Determine whether the...Ch. 5 - Prob. 2RE Ch. 5 - Ascent rate of a scuba diver Divers who ascend too...Ch. 5 - Use the tabulated values of f to estimate the...Ch. 5 - Estimate 144x+1dx by evaluating the left, right,...Ch. 5 - Prob. 6RE Ch. 5 - Estimating a definite integral Use a calculator...Ch. 5 - Suppose the expression lim0k=1n(xk3+xk)xk is the...Ch. 5 - Integration by Riemann sums Consider the integral...Ch. 5 - Limit definition of the definite integral Use the...Ch. 5 - Limit definition of the definite integral Use the...Ch. 5 - Limit definition of the definite integral Use the...Ch. 5 - Prob. 13RE Ch. 5 - Sum to integral Evaluate the following limit by...Ch. 5 - Symmetry properties Suppose that 04f(x)dx=10 and...Ch. 5 - Properties of integrals The figure shows the areas...Ch. 5 - Properties of integrals Suppose that 14f(x)dx=6,...Ch. 5 - Properties of integrals Suppose that 14f(x)dx=6,...Ch. 5 - Properties of integrals Suppose that 14f(x)dx=6,...Ch. 5 - Properties of integrals Suppose that 14f(x)dx=6,...Ch. 5 - Properties of integrals Suppose that 14f(x)dx=6,...Ch. 5 - Properties of integrals Suppose that 14f(x)dx=6,...Ch. 5 - Area by geometry Use geometry to evaluate the...Ch. 5 - Displacement by geometry Use geometry to find the...Ch. 5 - Area by geometry Use geometry to evaluate...Ch. 5 - Use geometry and properties of integrals to...Ch. 5 - Prob. 27RE Ch. 5 - Prob. 28RE Ch. 5 - Evaluate the following derivatives. 29....Ch. 5 - Evaluate the following derivatives....Ch. 5 - Evaluate the following derivatives. 31....Ch. 5 - Evaluate the following derivatives. 32....Ch. 5 - Evaluate the following derivatives. 33....Ch. 5 - Evaluate the following derivatives. 34....Ch. 5 - Find the intervals on which f(x)=x1(t3)(t6)11dt is...Ch. 5 - Area function by geometry Use geometry to find the...Ch. 5 - Given that F=f, use the substitution method to...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - 015re3r2+2dr Ch. 5 - sinzsin(cosz)dz Ch. 5 - ex+exdx Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - dx14x2 Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - 02cos2x6dx Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Prob. 71RE Ch. 5 - 33(511x17+302x13+117x9+303x3+x2)dx Ch. 5 - 1x2sin1xdx Ch. 5 - (tan1x)51+x2dx Ch. 5 - dx(tan1x)(1+x2)Ch. 5 - sin1x1x2dx Ch. 5 - x(x+3)10dx Ch. 5 - x7x4+1dx Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - Evaluating integrals Evaluate the following...Ch. 5 - 2/52/5dxx25x21 Ch. 5 - sin2x1+cos2xdx (Hint: sin2x=2sinxcosx.)Ch. 5 - 1010x200x2dx Ch. 5 - /2/2(cos2x+cosxsinx3sinx5)dx Ch. 5 - 04f(x)dx for f(x)={2x+1ifx33x2+2x8ifx3 Ch. 5 - 05|2x8|dx Ch. 5 - Prob. 87RE Ch. 5 - Area of regions Compute the area of the region...Ch. 5 - Prob. 89RE Ch. 5 - Prob. 90RE Ch. 5 - Prob. 91RE Ch. 5 - Area versus net area Find (i) the net area and...Ch. 5 - Gateway Arch The Gateway Arch in St Louis is 630...Ch. 5 - Root mean square The root mean square (or RMS) is...Ch. 5 - Displacement from velocity A particle moves along...Ch. 5 - Velocity to displacement An object travels on the...Ch. 5 - Find the average value of f(x)=e2xon [0, ln 2].Ch. 5 - Average height A baseball is launched into the...Ch. 5 - Average values Integration is not needed. a. 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