Calculus: trig functions anti-derivatives

In summary, the conversation involves solving for g(0) given g'(x) and g(1) with a given value of A. The antiderivative of g'(x) is found and a value for A is calculated, but there is a discrepancy in the final answer. The issue is resolved by adding a constant to the antiderivative and making sure the calculations are done in the correct unit mode.
  • #1
Melawrghk
145
0

Homework Statement


Let g'(x)=-17x16* sin(Ax9) - 9Ax25*cos(Ax9)

g(1)=143/9
Where A is a real number such that tanA=1/sqrt(80), 0<A<pi/2

Find g(0)

The Attempt at a Solution


I was able to get the antiderivative of g'(x), so that:
g(x) = -x17*sin(Ax9)

I got A=6.3794 degrees.

BUT, I don't get g(1)=143/9

What am I doing wrong? Did I assume wrong that the g'(x) was created by the product rule?
 
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  • #2
Melawrghk said:

Homework Statement


Let g'(x)=-17x16* sin(Ax9) - 9Ax25*cos(Ax9)

g(1)=143/9
Where A is a real number such that tanA=1/sqrt(80), 0<A<pi/2

Find g(0)

The Attempt at a Solution


I was able to get the antiderivative of g'(x), so that:
g(x) = -x17*sin(Ax9)

I got A=6.3794 degrees.

BUT, I don't get g(1)=143/9

What am I doing wrong? Did I assume wrong that the g'(x) was created by the product rule?

Your antiderivative looks fine. Did you remember to add a constant? IOW, you should have
g(x) = -x17*sin(Ax9) + C

You're sort of given A, and you're given that g(1) = 143/9, so you can find C. If you did all that, you can still run into problems calculating things with a calculator, such as when it's in radian mode but you're working with degrees.
 

1. What are the basic trigonometric functions used in calculus?

The basic trigonometric functions used in calculus are sine, cosine, tangent, cotangent, secant, and cosecant. These functions are used to represent the relationship between the sides and angles of a right triangle.

2. How are trigonometric functions used in calculus?

Trigonometric functions are used in calculus to model and solve various types of problems, such as calculating the rate of change, finding maximum and minimum values, and determining the area under a curve. They are also used in solving differential equations, which are fundamental in many areas of science and engineering.

3. What is the difference between a derivative and an anti-derivative?

A derivative is a mathematical concept that represents the rate of change of a function at a specific point. It is the slope of the tangent line to the function at that point. An anti-derivative, also known as an indefinite integral, is the reverse process of finding the original function from its derivative. It is denoted by the symbol ∫ and is used to find the area under a curve.

4. How are anti-derivatives of trigonometric functions calculated?

To calculate the anti-derivative of a trigonometric function, we use a set of rules known as integration formulas or techniques. These include substitution, integration by parts, trigonometric identities, and partial fractions. By applying these rules, we can find the anti-derivative of a trigonometric function and solve various types of problems in calculus.

5. What are some real-life applications of calculus and trigonometric functions?

Calculus and trigonometric functions have numerous real-life applications in fields such as physics, engineering, economics, and finance. For example, they are used to model and predict the motion of objects, design structures, optimize production processes, and analyze financial data. They are also essential in computer graphics and animation, enabling the creation of lifelike images and simulations.

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