To evaluate the transformation, let \( u = a + b - x \).
Then: \[ \frac{du}{dx} = -1 \quad \text{or} \quad dx = -du. \] When \( x = a \), \( u = b \); and when \( x = b \), \( u = a \).
The integral becomes: \[ \int_a^b f(x) \, dx = \int_b^a f(a + b - u) (-du). \]
Reversing the limits of integration, the negative sign is removed: \[ \int_a^b f(x) \, dx = \int_a^b f(a + b - x) \, dx. \]
Let A be the set of 30 students of class XII in a school. Let f : A -> N, N is a set of natural numbers such that function f(x) = Roll Number of student x.
On the basis of the given information, answer the followingIs \( f \) a bijective function?
On the basis of the following hypothetical data, calculate the percentage change in Real Gross Domestic Product (GDP) in the year 2022 – 23, using 2020 – 21 as the base year.
Year | Nominal GDP | Nominal GDP (Adjusted to Base Year Price) |
2020–21 | 3,000 | 5,000 |
2022–23 | 4,000 | 6,000 |