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Showing content from https://TheAlgorithms.github.io/C-Plus-Plus/d1/de9/integral__approximation_8cpp.html below:

TheAlgorithms/C++: math/integral_approximation.cpp File Reference

75 {

3.24, 7.56, [](

x) {

(x) +

(x) + x; });

78 std::cout << "Test Case 1" << std::endl;

79 std::cout << "function: log(x) + e^x + x" << std::endl;

80 std::cout << "range: [3.24, 7.56]" << std::endl;

std::cout <<

<<

<< std::endl;

83 std::cout << "Test 1 Passed!" << std::endl;

84 std::cout << "=====================" << std::endl;

85

x * x + cos(x) +

(x) +

(x) *

(x);

88 });

89 std::cout << "Test Case 2" << std::endl;

90 std::cout << "function: x^2 + cos(x) + e^x + log^2(x)" << std::endl;

91 std::cout << "range: [.023, 3.69]" << std::endl;

std::cout <<

<<

<< std::endl;

94 std::cout << "Test 2 Passed!" << std::endl;

95 std::cout << "=====================" << std::endl;

96

98 10.78, 24.899, [](const double x) { return x * x * x - x * x + 378; });

99 std::cout << "Test Case 3" << std::endl;

100 std::cout << "function: x^3 - x^2 + 378" << std::endl;

101 std::cout << "range: [10.78, 24.899]" << std::endl;

std::cout <<

<<

<< std::endl;

104 std::cout << "Test 3 Passed!" << std::endl;

105 std::cout << "=====================" << std::endl;

106

108 .101, .505,

[](

x) {

cos(x) * tan(x) * x * x +

(x); },

110 .00001);

111 std::cout << "Test Case 4" << std::endl;

112 std::cout << "function: cos(x)*tan(x)*x^2 + e^x" << std::endl;

113 std::cout << "range: [.101, .505]" << std::endl;

114 std::cout << "value: " << test_4 << std::endl;

116 std::cout << "Test 4 Passed!" << std::endl;

117 std::cout << "=====================" << std::endl;

118

-1, 1, [](

x) {

(-1 / (x * x)); });

121 std::cout << "Test Case 5" << std::endl;

122 std::cout << "function: e^(-1/x^2)" << std::endl;

123 std::cout << "range: [-1, 1]" << std::endl;

124 std::cout << "value: " << test_5 << std::endl;

126 std::cout << "Test 5 Passed!" << std::endl;

127}

void log(T msg)

A function to print given message on console.

uint256_t exp(uint256_t number, uint256_t power, const uint256_t &mod)

This function calculates number raised to exponent power under modulo mod using Modular Exponentiatio...

void test_eval(double approx, double expected, double threshold)

Wrapper to evaluate if the approximated value is within .XX% threshold of the exact value.

double integral_approx(double lb, double ub, const std::function< double(double)> &func, double delta=.0001)

Computes integral approximation.

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