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Photosynthesis The rate of primary production refers to the rate of conversion of inorganic carbon to organic carbon via photosynthesis. It is measured as a mass of carbon fixed per unit biomass, per unit time. A common model for this relationship is $$P(I)=\frac{a I}{\sqrt{1+b I^{2}}}$$ where $P$ is the rate of primary production as a function of light intensity $I$ . Suppose the light intensity changes withtime according to the equation $I(t)=k t,$ where $k$ is a constant(a) What is the rate of primary production as a function oftime? (b) What is the total amount of primary production over thefirst five units of time?

$| \frac{a}{b k}\left(\sqrt{1+25 b k^{2}}-1\right)$

Calculus 1 / AB

Calculus 2 / BC

Chapter 5

Integrals

Section 4

The Substitution Rule

Integration Techniques

Missouri State University

Campbell University

Oregon State University

Idaho State University

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

01:04

Photosynthesis Much of the…

02:03

05:33

Photosynthesis The rate (i…

03:26

Photosynthesis efficiency …

04:07

The rate (in $ mg $ $ car…

06:58

It is estimated that the n…

00:52

The formation of glucose f…

09:29

About $6.0 \times 10^{13} …

09:21

The following diagram summ…

02:18

Photosynthesis in plants c…

08:07

Photosynthesis produces gl…

06:08

07:06

The sun supplies energy at…

03:10

A single wavelength. Photo…

09:49

The net photosynthetic pro…

02:50

Photosynthesis can be divi…

01:52

08:24

In photosynthesis, plants …

00:51

Plants use the process of …

02:55

Let $M(t)$ be the mass (in…

Okay, So for this, all we have to do is rip State. Be integral from 0 to 5 off a Katie, a Katie divided by the square root off a one plus B a k t. And, um, this part here is squared. Right? That's it.

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03:14

Use a computer algebra system to evaluate the integral. Compare the answer w…

01:14

Evaluate the indefinite integral.$\int \frac{a+b x^{2}}{\sqrt{3 a x+b x^…

03:55

$59-62$ Produce graphs of $f$ that reveal all the important aspectsof th…

13:50

Use a graph to find approximate $x$ -coordinates of the points of intersecti…

00:21

What is wrong with the equation?$\int_{0}^{\pi} \sec ^{2} x d x=\tan x ]…

00:58

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10:37

Gene regulation In Section 10.3 a model of gene regulation is analyzed and i…

00:42

Evaluate the integral.$\int_{0}^{1} 10^{x} d x$

01:20

Evaluate the integral.$$\int \frac{1}{(t+4)(t-1)} d t$$

00:50

Evaluate the definite integral.$\int_{0}^{1}(3 t-1)^{50} d t$