To solve the integral ∫ 1−1(1 − y^2)^2 dy, we can follow these steps:

Step 1: Expand the expression inside the integral:
(1 − y^2)^2 = (1 − 2y^2 + y^4)

Step 2: Distribute the negative sign to the expression:
1−1(1 − y^2)^2 = 1 − (1 − 2y^2 + y^4)

Step 3: Simplify the expression:
1 − (1 − 2y^2 + y^4) = 1 − 1 + 2y^2 - y^4 = 2y^2 - y^4

Step 4: Integrate the simplified expression:
∫ (2y^2 - y^4) dy

Step 5: Apply the power rule of integration:
∫ (2y^2 - y^4) dy = (2/3)y^3 - (1/5)y^5 + C

Therefore, the solution to the integral ∫ 1−1(1 − y^2)^2 dy is (2/3)y^3 - (1/5)y^5 + C, where C is the constant of integration.

Question

To solve the integral ∫ 1−1(1 − y^2)^2 dy, we can follow these steps:

Step 1: Expand the expression inside the integral:
(1 − y^2)^2 = (1 − 2y^2 + y^4)

Step 2: Distribute the negative sign to the expression:
1−1(1 − y^2)^2 = 1 − (1 − 2y^2 + y^4)

Step 3: Simplify the expression:
1 − (1 − 2y^2 + y^4) = 1 − 1 + 2y^2 - y^4 = 2y^2 - y^4

Step 4: Integrate the simplified expression:
∫ (2y^2 - y^4) dy

Step 5: Apply the power rule of integration:
∫ (2y^2 - y^4) dy = (2/3)y^3 - (1/5)y^5 + C

Therefore, the solution to the integral ∫ 1−1(1 − y^2)^2 dy is (2/3)y^3 - (1/5)y^5 + C, where C is the constant of integration.

Knowee AI · Accepted Answer

To solve the integral ∫ 1−1(1 − y^2)^2 dy, we can follow these steps:

Step 1: Expand the expression inside the integral:
(1 − y^2)^2 = (1 − 2y^2 + y^4)

Step 2: Distribute the negative sign to the expression:
1−1(1 − y^2)^2 = 1 − (1 − 2y^2 + y^4)

Step 3: Simplify the expression:
1 − (1 − 2y^2 + y^4) = 1 − 1 + 2y^2 - y^4 = 2y^2 - y^4

Step 4: Integrate the simplified expression:
∫ (2y^2 - y^4) dy

Step 5: Apply the power rule of integration:
∫ (2y^2 - y^4) dy = (2/3)y^3 - (1/5)y^5 + C

Therefore, the solution to the integral ∫ 1−1(1 − y^2)^2 dy is (2/3)y^3 - (1/5)y^5 + C, where C is the constant of integration.

∫ 1−1(1 − y2)2 dy