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Chapter 4: Q. 3 (page 402)

Differential Equations: A differential equation is simply an equation that involves derivatives. The solution of a differential equation is the family of functions that make the differential equation true.

  • Solve the differential equation f'(x)=sinex. The solution will be a family of nonelementary functions.

Short Answer

Expert verified

Ans: The solution of the given differential equation isf(x)=Siex+C.

Step by step solution

01

Step 1. Given information: 

Consider the differential equation f'(x)=sinex

02

Step 2. Solving the differential equation :

Integrate on both sides

鈭�f'(x)=鈭�sinexdxf(x)=鈭�sinuudu鈭�u=sinexf(x)=Si(u)鈭�鈭�sinuudu=Si(u)f(x)=Siex+C

Here, Siex is the nonelementary function.

Hence, the solution of the given differential equation is f(x)=Siex+C

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Most popular questions from this chapter

Use integration formulas to solve each integral in Exercises 21鈥�62. You may have to use algebra, educated guess- and- check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. Check each of your answers by differentiating. (Hint for Exercise 54: tanx=sinxcosx).

鈭�(sec2x+csc2x)dx.

Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.

鈭�鈭�32鈥�1x+5dx

Suppose f(x)鈮�g(x)on [1, 3] and f(x)鈮�g(x)on (鈭掆垶, 1] and [3,鈭�). Write the area of the region between the graphs of f and g on [鈭�2, 5] in terms of definite integrals without using absolute values .

Describe an example that illustrates that 鈭�ab|f(x)|dx is not equal to |鈭�abf(x)dx|.

Without using absolute values, how many definite integrals would we need in order to calculate the area between the graphs of f(x) = sin x and g(x) = 12on [-蟺2,2蟺] ?
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