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Geometric Formula PROOF Integration problems
Area of a Triangle Formula Proof example question
Use Integration techniques in order to derive the formula for the Area of a Triangle, A, such that
where b is the base and h is the height.
Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!
Area of a Trapezoid Formula Proof example problem
Use Integration to derive the formula for the Area of a Trapezoid, A, such that
where b1 and b2 are bases and h is the height.
Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!
Area of a Circle Formula Proof example
Use Integration to derive the formula for the Area of a Circle, A, such that
where r is the radius.
Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!
Area of a Circle Formula Proof example question
Use Double Integration to prove the formula for the Area of a Circle, A, such that
where r is the radius.
Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!
Volume of a Sphere Formula Proof example problem
Use the Disk Integration method to derive the formula for the Volume of a Sphere, V, such that
where r is the radius.
Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!
Volume of a Cone Formula Proof example
Use the Disk Integration method to prove the formula for the Volume of a Right Circular Cone, V, such that
where r is the radius and h is the height.
Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!
Volume of a Torus Formula Proof example question
Use the Washer Integration method to derive the formula for the Volume of a Torus, V, such that
where r is the inner (minor) radius and R is the outer (major) radius.
Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!
Volume of a Torus Formula Proof example problem
Use the Shell Integration method to prove the formula for the Volume of a Torus, V, such that
where r is the inner (minor) radius and R is the outer (major) radius.
Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!
Surface Area of a Cone Formula Proof example
Use Integration to derive the formula for the Lateral Surface Area of a Right Circular Cone, SA, such that
where r is the radius and h is the height.
Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!
Surface Area of a Right Circular Cone Formula Proof with Double Integration example problem
Use Double Integrals to derive the formula for the Lateral Surface Area of a Right Circular Cone, SA, where
where r is the radius and h is the height.
Solution to this Calculus Geometric Formula Proof practice problem is provided in the video below!
Surface Area of a Sphere Formula Proof example question
Use Integration to prove the formula for the Surface Area of a Sphere, SA, such that
where r is the radius.
Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!
Volume of a Torus Formula Proof example
Use the Cylindrical Coordinates (Triple Integration) method to prove the formula for the Volume of a Torus, V, such that
where r is the inner (minor) radius and R is the outer (major) radius.
Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!
Volume of a Sphere Formula Proof example question
Use the Spherical Coordinates (Triple Integration) method to derive the formula for the Volume of a Sphere, V, such that
where r is the radius.
Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!
Volume of a Cone Formula Proof example problem
Use the Spherical Coordinates (Triple Integration) method to derive the formula for the Volume of a Right Circular Cone, V, such that
where r is the radius and h is the height.
Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!
Volume of a Torus Formula Proof example
Use the Spherical Coordinates (Triple Integration) method to prove the formula for the Volume of a Torus, V, such that
where r is the inner (minor) radius and R is the outer (major) radius.
Solution to this Calculus Geometric Formula Proof practice problem is given in the video below!
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