## 1. The integral ∫x dx is:

### Answer:

### Explanation:

The power of x increases by 1 and then we divide by the new power.

## 2. The integral of a constant 'c' is:

### Answer:

### Explanation:

The integration of a constant is the constant times x plus the arbitrary constant C.

## 3. The integral ∫(x^2 + 3x + 2) dx is:

### Answer:

### Explanation:

Each term is integrated separately using the power rule.

## 4. The integral ∫cos(x) dx is:

### Answer:

### Explanation:

The integral of cos(x) is sin(x).

## 5. Which of the following is an indefinite integral?

### Answer:

### Explanation:

Indefinite integrals do not have specified limits of integration.

## 6. The fundamental theorem of calculus connects:

### Answer:

### Explanation:

The theorem connects the concepts of differentiation and integration.

## 7. The integral ∫sec^2(x) dx is:

### Answer:

### Explanation:

The integral of sec^2(x) is tan(x).

## 8. Which symbol represents the integral operation?

### Answer:

### Explanation:

The symbol ∫ is used to represent integration.

## 9. The antiderivative of a function f(x) is given by:

### Answer:

### Explanation:

Antiderivative is another name for the indefinite integral.

## 10. ∫(d/dx of f(x)) dx is:

### Answer:

### Explanation:

Integrating the derivative of a function gives back the original function.

## 11. The area under the curve y = f(x) between x = a and x = b is given by:

### Answer:

### Explanation:

The definite integral gives the area under the curve between two limits.

## 12. The integral ∫sin^2(x) dx is:

### Answer:

### Explanation:

Use the identity sin^2(x) = (1 – cos(2x))/2 and then integrate.

## 13. If f'(x) = g(x), then ∫g(x) dx is:

### Answer:

### Explanation:

The integral of g(x) will be an antiderivative of f(x).

## 14. The integral of a sum is the sum of the integrals. This property is called:

### Answer:

### Explanation:

This property is fundamental to the linearity of the integral operation.

## 15. The method used to integrate the product of two functions is:

### Answer:

### Explanation:

Integration by parts is a technique used for the product of two functions.

## 16. The integral ∫e^x dx is:

### Answer:

### Explanation:

The integral of e^x is itself e^x.

## 17. The integral ∫ln(x) dx is:

### Answer:

### Explanation:

The integration of ln(x) yields xln(x) minus x.

## 18. If ∫f(x) dx = F(x) + C, then F(x) is:

### Answer:

### Explanation:

F(x) represents the antiderivative of the function f(x).

## 19. The integral ∫(1/x) dx, x > 0, is:

### Answer:

### Explanation:

The integral of 1/x for positive x is the natural logarithm of x.

## 20. The area between two curves y = f(x) and y = g(x) from x = a to x = b is given by:

### Answer:

### Explanation:

The area is the difference of the two functions, but the order depends on which function lies above the other in the given interval.