to which of the following does the integral course hero

What is the integral of 1/x from AC to bc(0 < A < B)?

Show that if c > 0, then the integral of 1/x from ac to bc (0 < a < b) is the same as the integral of 1/x from a to b. The following exercises are intended to derive the fundamental properties of the natural log starting from the definition ln(x) = ∫x 1dt t, using properties of the definite integral and making no further assumptions. 383.

What is integrated integral calculus?

Integral calculus gives us the tools to answer these questions and many more. Surprisingly, these questions are related to the derivative, and in some sense, the answer to each one is the opposite of the derivative.

How do you write integrals in terms of compositions with logarithms?

Write an integral to express the area under the graph of y = et between t = 0 and t = lnx, and evaluate the integral. In the following exercises, use appropriate substitutions to express the trigonometric integrals in terms of compositions with logarithms.

A brief introduction to integral calculus

How do you find the area under a curve? What about the length of any curve? Is there a way to make sense out of the idea of adding infinitely many infinitely small things? Integral calculus gives us the tools to answer these questions and many more.

Series

Test your knowledge of the skills in this course. Have a test coming up? The Course challenge can help you understand what you need to review.

Which function is the most efficient?

The exponential function is perhaps the most efficient function in terms of the operations of calculus. The exponential function, y = ex, is its own derivative and its own integral.

What is the value of x = N + 1?

x = N + 1 is, at most, 0.01.

Can exponential functions be integrated?

Exponential functions can be integrated using the following formulas.