Integral of sin(lnx) + (lnx)^3/2 w.r.t. x

Thread starter sapiental
Start date Oct 9, 2006
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Derivative Integral

In summary, the integral of sin(lnx) + (lnx)^3/2 w.r.t. x is a fundamental concept in calculus that represents the area under the curve of the function and is important in solving a wide range of problems in various fields. It can be solved using integration techniques or online tools and has a physical interpretation as the total change or accumulation of a quantity. It can be both a definite and indefinite integral, depending on the context.

Oct 9, 2006

sapiental

g(x) = integral 0 to lnx (sin(t)+t^3/2))dt

find d/dx g(x):

let u = lnx

= sin(u) + u^3/2 du/dx
= sin(lnx)(1/x) + x^3/2(1/x)

Thanks

Last edited: Oct 9, 2006

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Oct 9, 2006

HallsofIvy

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What is your question?

Oct 9, 2006

drpizza

I believe what you need to examine is the fundamental theorem of calculus, part 2. Check your text.

edit: in that section, you'll probably see some examples where they find the derivative of the integral of some function...

Last edited: Oct 9, 2006

FAQ: Integral of sin(lnx) + (lnx)^3/2 w.r.t. x

What is the integral of sin(lnx) + (lnx)^3/2 w.r.t. x?

The integral of sin(lnx) + (lnx)^3/2 w.r.t. x is a mathematical expression that represents the area under the curve of the function sin(lnx) + (lnx)^3/2. It is a fundamental concept in calculus that is used to find the total change or accumulation of a function over a given interval.

Why is the integral of sin(lnx) + (lnx)^3/2 w.r.t. x important?

The integral of sin(lnx) + (lnx)^3/2 w.r.t. x is important because it allows us to solve a wide range of problems in physics, engineering, and other fields that involve finding the total change of a quantity over a given interval. It is also an essential tool in evaluating areas, volumes, and other geometric properties.

How do you solve the integral of sin(lnx) + (lnx)^3/2 w.r.t. x?

To solve the integral of sin(lnx) + (lnx)^3/2 w.r.t. x, you can use integration techniques such as substitution, integration by parts, or trigonometric identities. You can also use online integration calculators or software programs to find the exact value of the integral.

What is the physical interpretation of the integral of sin(lnx) + (lnx)^3/2 w.r.t. x?

The physical interpretation of the integral of sin(lnx) + (lnx)^3/2 w.r.t. x is the total change or accumulation of a quantity represented by the function sin(lnx) + (lnx)^3/2 over a given interval. In practical terms, this could represent the displacement, velocity, or acceleration of an object over time.

Is the integral of sin(lnx) + (lnx)^3/2 w.r.t. x a definite or indefinite integral?

The integral of sin(lnx) + (lnx)^3/2 w.r.t. x can be both a definite and indefinite integral, depending on the context of the problem. A definite integral has specific limits of integration, while an indefinite integral does not. In general, the indefinite integral represents the antiderivative of the given function, while the definite integral represents the area under the curve of the function over a given interval.