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ori
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integral
S (-sin(t))* exp(cos^3(t)) dt
t from 0 to 2pi
how do i solve it?
10x
S (-sin(t))* exp(cos^3(t)) dt
t from 0 to 2pi
how do i solve it?
10x
Integral S (-sin(t))* exp(cos^3(t)) dt
- Thread starter ori
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- Integral
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SUMMARY
The integral of the function S (-sin(t)) * exp(cos^3(t)) dt from 0 to 2π evaluates to 0. This conclusion is derived from the properties of the sine function, where the integral of sin(t) over a full period (0 to 2π) is zero. The negative sine function maintains this property, as the exponential factor exp(cos^3(t)) does not affect the overall symmetry of the integral across the specified interval.
PREREQUISITES- Understanding of integral calculus
- Familiarity with trigonometric functions
- Knowledge of exponential functions
- Concept of symmetry in integrals
- Study the properties of definite integrals involving trigonometric functions
- Learn about the impact of symmetry on integrals
- Explore advanced techniques in integral calculus
- Investigate the behavior of exponential functions in integrals
Students of calculus, mathematicians, and anyone interested in solving integrals involving trigonometric and exponential functions.
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