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When one type of data is assigned to another type of variable, an implicit type conversion will take place automatically if The two types are compatible The destination type has a range that is greater than the source type When these two conditions are met, a widening conversion takes place For example, the int type is always large enough to hold all valid byte values, and both int and byte are compatible integer types, so an implicit conversion can be applied For widening conversions, the numeric types, including integer and floating-point types, are compatible with each other For example, the following program is perfectly valid since long to double is a widening conversion that is automatically performed

SOLUTION For clarity we set (x) = 3 sin x 4, (x) = 3(cos x) The integral then has the form 1 1 (x) dx = ln | (x)| + C 3 (x) 3 Resubstituting the expression for (x) yields that 1 cos x dx = ln |3 sin x 4| + C 3 sin x 4 3 You Try It: Evaluate EXAMPLE 66

// Demonstrate implicit conversion from long to double using System; class LtoD { static void Main() { long L; double D; L = 100123285L; D = L; ConsoleWriteLine("L and D: " + L + " " + D); } }

All models are wrong Some models are useful George Box Everything should be made as simple as possible, but not simpler Albert Einstein

Part I:

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Although there is an implicit conversion from long to double, there is no implicit conversion from double to long since this is not a widening conversion Thus, the following version of the preceding program is invalid:

For clarity we take (x) = sin x, (x) = cos x Then the integral becomes (x) dx = ln | (x)| + C (x) Resubstituting the expression for yields the solution: cot x dx = ln | sin x| + C

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// *** This program will not compile *** using System; class LtoD { static void Main() { long L; double D; D = 1001232850; L = D; // Illegal!!! ConsoleWriteLine("L and D: " + L + " " + D); } }

In addition to the restrictions just described, there are no implicit conversions between decimal and float or double, or from the numeric types to char or bool Also, char and bool are not compatible with each other

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