tan(θ) = x 3 Video Example EXAMPLE 3 Find 1 x2 x2 + 9 dx . SOLUTION Let x = 3 tan(θ), −π/2 < θ < π/2. Then dx = dθ and x2 + 9 = 9 tan2(θ) + 9 = 9 sec2(θ) = 3|sec(θ)| = 3 sec(θ). Thus we have dx x2 x2 + 9 = dθ 9 tan2(θ) · 3 sec(θ) = 1 9 tan2(θ) dθ. To evaluate this trigonometric integral we put everything in terms of sin(θ) and cos(θ). sec(θ) tan2(θ) = 1 · cos2(θ) sin2(θ) = sin2(θ) Therefore, making the substitution u = sin(θ), we have dx x2 x2 + 9 = 1 9

/is used for a fraction 1) if x = 2/3 and y = 3/4, what is the value of (x + y) (x/y) expressed as a common fraction? 2) what is the least positive integer greater than 1 that leaves a remainder of 1 when divided by each of 2, 3, 4, 5, 6, 7, 8, and 9? 3) the ponde family's powerjet pumps 420 gallons of water per hour. at this rate, how many gallons of water will it pump in 45 minutes? 4) kim's insurance company pays 80% of the cost of all prescription medication she purchases in a year beyond the first $250 worth of prescriptions. her prescriptions for this year cost a total of $570. how many dollars of this amounts will kim's insurance company pay?

What set does not contain -3 the set of all real numbers the set of all integers the set of all whole numbers the set of all rational numbers

Leslie started last week with $1200 in her checking account. during the week, she wrote the checks below.