Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Evaluate the integral.
$ \displaystyle \int t \csc^2 t dt $
Get the answer to your homework problem.
Try Numerade free for 7 days
$-t \cot t+\ln |z|+C=-t \cot t+\ln |\sin t|+C$
Calculus 2 / BC
Techniques of Integration
Integration by Parts
Missouri State University
Oregon State University
Harvey Mudd College
In mathematics, integration is one of the two main operations in calculus, with its inverse, differentiation, being the other. Given a function of a real variable, an antiderivative, integral, or integrand is the function's derivative, with respect to the variable of interest. The integrals of a function are the components of its antiderivative.
The definite integral of a function from a to b is the area of the region in the xy-plane that lies between the graph of the function and the x-axis, above the x-axis, or below the x-axis.
The indefinite integral of a function is an antiderivative of the function, and can be used to find the original function when given the derivative. The definite integral of a function is a single-valued function on a given interval. It can be computed by evaluating the definite integral of a function at every x in the domain of the function, then adding the results together.
In mathematics, a technique is a method or formula for solving a problem. Techniques are often used in mathematics, physics, economics, and computer science.
Evaluate the integral.…
Find the indefinite integr…
Evaluate the indefinite in…
Find the general indefinit…
Evaluate the integrals…
Evaluate each integral.
The problem is evaluated the integral t times per second t square dt. This problem. We will use the method of integration by parts, so the formula is integral: u from dx is equal to: u times, v minus the integral of u prime v d x. Now for our problem, we can let? U is equal to p and the prime is equal to second square. Then u, prim is equal to 1 and v is equal to negative cotananttnow, integral o f t times. Second t square dt is equal to u times so this is negative to tangent t minus integral of 1 times negative cotangent t, but this is equal to negative 2 tandant t minus this is past minus minus co. Tangent to this pass integral of co tangent to we can write cotangent t as cosine t over sine t t now for this integral. We can use? U substitution, that? U is equal to sine t, then du equal to cosine t, so this integral is equal to integral 1 over. U u! This is not. Of this is absolute value of sine t now integral of t cosecant square. This is equal to negative t. Co, tangent t plus in absolute value of sine t and pass con number c.
View More Answers From This Book
Find Another Textbook
'8.(10 Points) We measure for resistance R of each resistor in a produc…
"A random sample is drawn from a population with mean / =76 and standar…
'Twenty samples of water were drawn from a public works building in Nov…
"spherical balloon is inflated with gas at the rate of 800 cubic centim…
'For a factor X with d categories the one-factor mean function isE(…
'Suppose that the number of trials of = Binomial Distribution and the p…
'The figure shows a 1325-yard-long sand beach and an oil platform in th…
'16. Two kinds of crated cargo, A and B, are to be shipped by truck The…
'At what nominal rate compounded continuously must money be invested t0…