Proving the Integral Formula for Powers of Sine for the Perplexed

Thread starter r4sph4sp
Start date Nov 21, 2010
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Integrals Trigonometry

In summary, trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. The basic trigonometric functions, sine, cosine, and tangent, represent the ratios of sides in a right triangle and are used to calculate angles and side lengths. Trigonometry has many real-life applications in fields such as engineering, physics, and astronomy. An integral in calculus represents the area under a curve on a graph and is used to find the total value of a function over a given interval. Trigonometric integrals, which involve integrating functions with trigonometric components, are used to solve problems involving areas, volumes, and other geometric shapes, as well as in many applications in physics and engineering.

Nov 21, 2010

r4sph4sp

I need help with a question and I'm totally stuck at this! My friends can't help me so you are my last way out!

Prove

∫sin^n x dx= -(1/n)cos x sin^n-1 x + ((n-1)/n) ∫sin^n-2 x dx

Thanks for your time!

Sincerely :)

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Nov 21, 2010

micromass

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I see a product: [tex]\sin(x)\sin^{n-1}(x)[/tex]. Try partial integration on that...

FAQ: Proving the Integral Formula for Powers of Sine for the Perplexed

What is trigonometry?

Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It is used to solve problems involving right triangles and can also be applied to non-right triangles.

What are the basic trigonometric functions?

The basic trigonometric functions are sine, cosine, and tangent. These functions represent the ratios of the sides of a right triangle and are used to calculate angles and side lengths.

How is trigonometry used in real life?

Trigonometry has many practical applications in fields such as engineering, physics, and astronomy. It is used to calculate distances and heights, analyze motion and forces, and design structures.

What is an integral in calculus?

An integral is a mathematical concept that represents the area under a curve on a graph. It is used to find the total value of a function over a given interval and is an important tool in solving problems involving rates of change.

How are trigonometric integrals used?

Trigonometric integrals involve integrating functions that contain trigonometric functions. They are used to solve problems involving areas, volumes, and other geometric shapes, as well as in many applications in physics and engineering.