The integral ∫ −1/2 (6−x)dx can be solved as follows:

Step 1: Distribute the -1/2 inside the parentheses to get -1/2 * 6 + 1/2 * x which simplifies to -3 + 1/2 * x.

Step 2: Now, the integral becomes ∫ (-3 + 1/2 * x) dx.

Step 3: Break up the integral into two separate integrals: ∫ -3 dx + ∫ 1/2 * x dx.

Step 4: Integrate each part separately. The integral of -3 dx is -3x. The integral of 1/2 * x dx is 1/4 * x^2.

Step 5: So, the integral ∫ −1/2 (6−x)dx = -3x + 1/4 * x^2 + C, where C is the constant of integration.

Question

The integral ∫ −1/2 (6−x)dx can be solved as follows:

Step 1: Distribute the -1/2 inside the parentheses to get -1/2 * 6 + 1/2 * x which simplifies to -3 + 1/2 * x.

Step 2: Now, the integral becomes ∫ (-3 + 1/2 * x) dx.

Step 3: Break up the integral into two separate integrals: ∫ -3 dx + ∫ 1/2 * x dx.

Step 4: Integrate each part separately. The integral of -3 dx is -3x. The integral of 1/2 * x dx is 1/4 * x^2.

Step 5: So, the integral ∫ −1/2 (6−x)dx = -3x + 1/4 * x^2 + C, where C is the constant of integration.

Knowee AI · Accepted Answer

The integral ∫ −1/2 (6−x)dx can be solved as follows:

Step 1: Distribute the -1/2 inside the parentheses to get -1/2 * 6 + 1/2 * x which simplifies to -3 + 1/2 * x.

Step 2: Now, the integral becomes ∫ (-3 + 1/2 * x) dx.

Step 3: Break up the integral into two separate integrals: ∫ -3 dx + ∫ 1/2 * x dx.

Step 4: Integrate each part separately. The integral of -3 dx is -3x. The integral of 1/2 * x dx is 1/4 * x^2.

Step 5: So, the integral ∫ −1/2 (6−x)dx = -3x + 1/4 * x^2 + C, where C is the constant of integration.

∫ −12 (6−x)dx